feat(lessons): add lessons from client db
This commit is contained in:
shafin-r
492
src/pages/student/lessons/CirclePropertiesLesson.tsx
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492
src/pages/student/lessons/CirclePropertiesLesson.tsx
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import React, { useRef, useState, useEffect } from "react";
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import { ArrowDown, Check, BookOpen, Target, Layers } from "lucide-react";
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import CircleTheoremsWidget from "../../../components/lessons/CircleTheoremsWidget";
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import TangentPropertiesWidget from "../../../components/lessons/TangentPropertiesWidget";
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import PowerOfPointWidget from "../../../components/lessons/PowerOfPointWidget";
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import Quiz from "../../../components/lessons/Quiz";
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import { CIRCLE_PROP_QUIZ_DATA } from "../../../utils/constants";
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import { Frac } from "../../../components/Math";
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interface LessonProps {
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onFinish?: () => void;
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}
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const CirclePropertiesLesson: React.FC<LessonProps> = ({ onFinish }) => {
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const [activeSection, setActiveSection] = useState(0);
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const sectionsRef = useRef<(HTMLElement | null)[]>([]);
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const scrollToSection = (index: number) => {
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setActiveSection(index);
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sectionsRef.current[index]?.scrollIntoView({
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behavior: "smooth",
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block: "start",
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});
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};
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useEffect(() => {
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const observer = new IntersectionObserver(
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(entries) => {
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entries.forEach((entry) => {
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if (entry.isIntersecting) {
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const index = sectionsRef.current.indexOf(
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entry.target as HTMLElement,
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);
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if (index !== -1) setActiveSection(index);
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}
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});
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},
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{ rootMargin: "-20% 0px -60% 0px" },
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);
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sectionsRef.current.forEach((section) => {
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if (section) observer.observe(section);
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});
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return () => observer.disconnect();
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}, []);
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const SectionMarker = ({
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index,
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title,
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icon: Icon,
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}: {
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index: number;
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title: string;
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icon: any;
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}) => {
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const isActive = activeSection === index;
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const isPast = activeSection > index;
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return (
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<button
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onClick={() => scrollToSection(index)}
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className={`flex items-center gap-3 p-3 w-full rounded-lg transition-all ${isActive ? "bg-white shadow-md border border-violet-100" : "hover:bg-slate-100"}`}
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>
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<div
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className={`w-8 h-8 rounded-full flex items-center justify-center shrink-0 ${isActive ? "bg-violet-600 text-white" : isPast ? "bg-violet-400 text-white" : "bg-slate-200 text-slate-500"}`}
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>
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{isPast ? (
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<Check className="w-4 h-4" />
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) : (
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<Icon className="w-4 h-4" />
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)}
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</div>
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<div className="text-left">
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<p
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className={`text-sm font-bold ${isActive ? "text-violet-900" : "text-slate-600"}`}
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>
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{title}
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</p>
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</div>
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</button>
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);
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};
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return (
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<div className="flex flex-col lg:flex-row min-h-screen">
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<aside className="w-full lg:w-64 lg:fixed lg:top-20 lg:bottom-0 lg:overflow-y-auto p-4 border-r border-slate-200 bg-slate-50 z-0 hidden lg:block">
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<nav className="space-y-2">
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<SectionMarker index={0} title="Central vs Inscribed" icon={Target} />
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<SectionMarker index={1} title="Tangents" icon={Layers} />
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<SectionMarker index={2} title="Power of a Point" icon={BookOpen} />
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<SectionMarker index={3} title="Practice" icon={BookOpen} />
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</nav>
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</aside>
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<div className="flex-1 lg:ml-64 p-6 md:p-12 max-w-4xl mx-auto">
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{/* Section 1: Central vs Inscribed Angles */}
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<section
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ref={(el) => {
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sectionsRef.current[0] = el;
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}}
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className="min-h-screen flex flex-col justify-center mb-24 pt-20 lg:pt-0"
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>
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<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
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Central vs. Inscribed Angles
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</h2>
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<div className="prose prose-slate text-lg text-slate-600 mb-8">
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<p>
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Circle angle theorems are among the highest-frequency SAT topics.
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The core relationship is simple: angles and arcs are linked by a
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factor of 2.
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</p>
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</div>
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<div className="bg-violet-50 border border-violet-200 rounded-2xl p-6 mb-8 space-y-5">
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<h3 className="text-lg font-bold text-violet-900">
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The Central vs. Inscribed Relationship
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</h3>
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<div className="grid md:grid-cols-2 gap-4">
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<div className="bg-white rounded-xl p-5 border border-violet-200">
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<p className="font-bold text-violet-900 mb-1">Central Angle</p>
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<p className="text-sm text-slate-700 mb-2">
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Vertex at the <strong>center</strong>. Degree measure equals
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the intercepted arc.
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</p>
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<div className="font-mono text-center bg-violet-50 py-2 rounded text-violet-700 font-bold">
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∠central = arc°
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</div>
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<p className="text-xs text-slate-500 mt-2">
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Example: Central angle = 80° → arc = 80°
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</p>
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</div>
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<div className="bg-indigo-50 rounded-xl p-5 border border-indigo-200">
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<p className="font-bold text-indigo-900 mb-1">
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Inscribed Angle
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</p>
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<p className="text-sm text-slate-700 mb-2">
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Vertex on the <strong>circle</strong>. Measure is exactly half
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the intercepted arc.
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</p>
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<div className="font-mono text-center bg-indigo-50 py-2 rounded text-indigo-700 font-bold">
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∠inscribed = <Frac n="arc°" d="2" />
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</div>
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<p className="text-xs text-slate-500 mt-2">
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Example: Arc = 120° → inscribed angle = 60°
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</p>
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</div>
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</div>
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{/* Key Corollaries */}
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<div className="bg-white rounded-xl p-5 border border-violet-100">
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<p className="font-bold text-violet-800 mb-3">
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Key Corollaries (SAT Favorites)
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</p>
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<div className="space-y-2">
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<div className="bg-violet-50 rounded-lg p-3 text-sm">
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<p className="font-semibold text-violet-800 mb-1">
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Thales' Theorem
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</p>
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<p className="text-slate-700">
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An inscribed angle that intercepts a{" "}
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<strong>semicircle</strong> (its chord is a diameter) is
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always <strong>90°</strong>. If you see a triangle inscribed
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in a circle where one side is the diameter, the opposite
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angle is 90°.
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</p>
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</div>
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<div className="bg-violet-50 rounded-lg p-3 text-sm">
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<p className="font-semibold text-violet-800 mb-1">
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Inscribed Angles on the Same Arc
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</p>
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<p className="text-slate-700">
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All inscribed angles intercepting the same arc are equal,
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regardless of where on the circle the vertex sits.
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</p>
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</div>
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<div className="bg-violet-50 rounded-lg p-3 text-sm">
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<p className="font-semibold text-violet-800 mb-1">
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Cyclic Quadrilateral
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</p>
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<p className="text-slate-700">
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Opposite angles in a quadrilateral inscribed in a circle sum
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to 180°. So ∠A + ∠C = 180° and ∠B + ∠D = 180°.
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</p>
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</div>
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</div>
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</div>
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{/* Worked Examples */}
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<div className="space-y-3">
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<div className="bg-sky-50 rounded-xl p-4 border border-sky-200 text-sm">
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<p className="font-semibold text-sky-800 mb-2">
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Worked Example 1: Find inscribed angle
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</p>
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<div className="font-mono text-xs text-slate-700 space-y-1">
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<p>
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A central angle is 110°. An inscribed angle intercepts the
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same arc. Find the inscribed angle.
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</p>
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<p>Arc = 110° (central angle equals arc)</p>
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<p>
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Inscribed angle = <Frac n="110°" d="2" /> ={" "}
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<strong className="text-sky-800">55°</strong>
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</p>
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</div>
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</div>
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<div className="bg-sky-50 rounded-xl p-4 border border-sky-200 text-sm">
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<p className="font-semibold text-sky-800 mb-2">
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Worked Example 2: Cyclic quadrilateral
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</p>
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<div className="font-mono text-xs text-slate-700 space-y-1">
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<p>
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Quadrilateral ABCD is inscribed in a circle. ∠A = 75°, ∠B =
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85°. Find ∠C and ∠D.
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</p>
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<p>
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∠C = 180° − 75° ={" "}
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<strong className="text-sky-800">105°</strong> (opposite to
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A)
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</p>
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<p>
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∠D = 180° − 85° ={" "}
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<strong className="text-sky-800">95°</strong> (opposite to
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B)
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</p>
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</div>
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</div>
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</div>
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</div>
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<CircleTheoremsWidget />
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<button
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onClick={() => scrollToSection(1)}
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className="mt-12 group flex items-center text-violet-600 font-bold hover:text-violet-800 transition-colors"
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>
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Next: Tangent Properties{" "}
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<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
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</button>
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</section>
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{/* Section 2: Tangents */}
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<section
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ref={(el) => {
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sectionsRef.current[1] = el;
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}}
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className="min-h-screen flex flex-col justify-center mb-24"
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>
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<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
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Tangent Properties
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</h2>
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<div className="prose prose-slate text-lg text-slate-600 mb-8">
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<p>
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A tangent line touches the circle at exactly one point (the point
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of tangency). Two critical theorems govern all SAT tangent
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questions.
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</p>
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</div>
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<div className="bg-violet-50 border border-violet-200 rounded-2xl p-6 mb-8 space-y-5">
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<h3 className="text-lg font-bold text-violet-900">
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Two Fundamental Tangent Theorems
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</h3>
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<div className="space-y-3">
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<div className="bg-white rounded-xl p-5 border border-violet-200">
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<p className="font-bold text-violet-900 mb-2">
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Property 1: Tangent-Radius Perpendicularity
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</p>
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<p className="text-sm text-slate-700 mb-2">
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A radius drawn to the point of tangency is always{" "}
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<strong>perpendicular</strong> to the tangent line — they form
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a 90° angle. This creates a right triangle you can use with
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the Pythagorean theorem.
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</p>
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<div className="bg-violet-50 rounded-lg p-3 text-sm">
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<p className="font-semibold text-violet-700 mb-1">
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Worked Example:
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</p>
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<div className="font-mono text-xs text-slate-700 space-y-1">
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<p>
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External point P is 13 units from center O. Radius = 5.
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Find tangent length PT.
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</p>
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<p>PT² + r² = PO² (right angle at T)</p>
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<p>PT² + 25 = 169</p>
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<p>
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PT = √144 ={" "}
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<strong className="text-violet-700">12</strong>
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</p>
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</div>
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</div>
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</div>
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<div className="bg-white rounded-xl p-5 border border-violet-200">
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<p className="font-bold text-violet-900 mb-2">
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Property 2: Two Tangents from One External Point
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</p>
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<p className="text-sm text-slate-700 mb-2">
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If two tangent segments are drawn from the same external
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point, they are <strong>equal in length</strong>. If PA and PB
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are both tangents from P, then PA = PB.
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</p>
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<div className="bg-violet-50 rounded-lg p-3 text-sm">
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<p className="font-semibold text-violet-700 mb-1">
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Worked Example:
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</p>
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<div className="font-mono text-xs text-slate-700 space-y-1">
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<p>
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From external point P, tangent PA = 3x + 2 and tangent PB
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= 5x − 4.
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</p>
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<p>Set equal: 3x + 2 = 5x − 4</p>
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<p>6 = 2x → x = 3</p>
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<p>
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PA = PB = <strong className="text-violet-700">11</strong>
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</p>
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</div>
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</div>
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</div>
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</div>
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{/* SAT Trap */}
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<div className="bg-red-50 border border-red-200 rounded-xl p-4 text-sm">
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<p className="font-bold text-red-900 mb-1">
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SAT Trap: Don't Confuse Tangent Line with Tangent Segment
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</p>
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<p className="text-slate-700">
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The "two tangents are equal" rule applies to the{" "}
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<em>segments</em> from the external point to the points of
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tangency — not to the full tangent lines extending beyond the
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circle.
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</p>
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</div>
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</div>
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<TangentPropertiesWidget />
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<button
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onClick={() => scrollToSection(2)}
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className="mt-12 group flex items-center text-violet-600 font-bold hover:text-violet-800 transition-colors"
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>
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Next: Power of a Point{" "}
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<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
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</button>
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</section>
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{/* Section 3: Power of a Point */}
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<section
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||||
ref={(el) => {
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sectionsRef.current[2] = el;
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}}
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className="min-h-screen flex flex-col justify-center mb-24"
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>
|
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<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
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Power of a Point
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</h2>
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<div className="prose prose-slate text-lg text-slate-600 mb-8">
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<p>
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"Power of a Point" relates segment lengths when lines pass through
|
||||
or near a circle. Two main cases appear on the SAT.
|
||||
</p>
|
||||
</div>
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||||
|
||||
<div className="bg-violet-50 border border-violet-200 rounded-2xl p-6 mb-8 space-y-5">
|
||||
<h3 className="text-lg font-bold text-violet-900">
|
||||
The Two Power-of-a-Point Cases
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</h3>
|
||||
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||||
<div className="grid md:grid-cols-2 gap-4">
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||||
<div className="bg-white rounded-xl p-5 border border-violet-200">
|
||||
<p className="font-bold text-violet-900 mb-1">
|
||||
Case 1: Chord-Chord (Inside)
|
||||
</p>
|
||||
<p className="text-sm text-slate-700 mb-2">
|
||||
Two chords intersect inside the circle at point P.
|
||||
</p>
|
||||
<div className="font-mono text-center bg-violet-50 py-2 rounded text-violet-700 font-bold">
|
||||
a × b = c × d
|
||||
</div>
|
||||
<p className="text-xs text-slate-500 mt-2">
|
||||
a and b are the two segments of one chord; c and d are the two
|
||||
segments of the other.
|
||||
</p>
|
||||
</div>
|
||||
<div className="bg-indigo-50 rounded-xl p-5 border border-indigo-200">
|
||||
<p className="font-bold text-indigo-900 mb-1">
|
||||
Case 2: Secant-Secant or Tangent-Secant (Outside)
|
||||
</p>
|
||||
<p className="text-sm text-slate-700 mb-2">
|
||||
Two secants, or a tangent and secant, from external point P.
|
||||
</p>
|
||||
<div className="font-mono text-center bg-indigo-50 py-2 rounded text-indigo-700 font-bold">
|
||||
ext₁ × whole₁ = ext₂ × whole₂
|
||||
</div>
|
||||
<p className="text-xs text-slate-500 mt-2">
|
||||
For tangent: tangent² = ext × whole (since both segments of
|
||||
the tangent chord are equal).
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
{/* Worked Examples */}
|
||||
<div className="space-y-3">
|
||||
<div className="bg-sky-50 rounded-xl p-4 border border-sky-200 text-sm">
|
||||
<p className="font-semibold text-sky-800 mb-2">
|
||||
Worked Example 1: Chord-Chord
|
||||
</p>
|
||||
<div className="font-mono text-xs text-slate-700 space-y-1">
|
||||
<p>
|
||||
Two chords intersect inside. Chord 1 has segments 4 and 9.
|
||||
Chord 2 has segments 6 and x.
|
||||
</p>
|
||||
<p>4 × 9 = 6 × x</p>
|
||||
<p>
|
||||
36 = 6x → x = <strong className="text-sky-800">6</strong>
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
<div className="bg-sky-50 rounded-xl p-4 border border-sky-200 text-sm">
|
||||
<p className="font-semibold text-sky-800 mb-2">
|
||||
Worked Example 2: Tangent-Secant
|
||||
</p>
|
||||
<div className="font-mono text-xs text-slate-700 space-y-1">
|
||||
<p>
|
||||
From external point P: tangent PT = 6, secant passes through
|
||||
circle with external part = 4 and whole length = x.
|
||||
</p>
|
||||
<p>PT² = ext × whole</p>
|
||||
<p>6² = 4 × x</p>
|
||||
<p>
|
||||
36 = 4x → x = <strong className="text-sky-800">9</strong>
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
<div className="bg-sky-50 rounded-xl p-4 border border-sky-200 text-sm">
|
||||
<p className="font-semibold text-sky-800 mb-2">
|
||||
Worked Example 3: Secant-Secant
|
||||
</p>
|
||||
<div className="font-mono text-xs text-slate-700 space-y-1">
|
||||
<p>
|
||||
Two secants from P: first has external 3, whole 12. Second
|
||||
has external 4, whole x.
|
||||
</p>
|
||||
<p>3 × 12 = 4 × x</p>
|
||||
<p>
|
||||
36 = 4x → x = <strong className="text-sky-800">9</strong>
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<PowerOfPointWidget />
|
||||
|
||||
<button
|
||||
onClick={() => scrollToSection(3)}
|
||||
className="mt-12 group flex items-center text-violet-600 font-bold hover:text-violet-800 transition-colors"
|
||||
>
|
||||
Next: Practice Quiz{" "}
|
||||
<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
|
||||
</button>
|
||||
</section>
|
||||
|
||||
{/* Section 4: Quiz */}
|
||||
<section
|
||||
ref={(el) => {
|
||||
sectionsRef.current[3] = el;
|
||||
}}
|
||||
className="min-h-screen flex flex-col justify-center"
|
||||
>
|
||||
<h2 className="text-4xl font-extrabold text-slate-900 mb-8">
|
||||
Practice Time
|
||||
</h2>
|
||||
{CIRCLE_PROP_QUIZ_DATA.map((quiz, idx) => (
|
||||
<div key={quiz.id} className="mb-12">
|
||||
<Quiz data={quiz} />
|
||||
</div>
|
||||
))}
|
||||
<div className="p-8 bg-violet-900 rounded-2xl text-white text-center mt-12">
|
||||
<h3 className="text-2xl font-bold mb-4">Topic Mastered!</h3>
|
||||
<button
|
||||
onClick={onFinish}
|
||||
className="px-6 py-3 bg-white text-violet-900 font-bold rounded-full hover:bg-violet-50 transition-colors"
|
||||
>
|
||||
Finish Lesson ✓
|
||||
</button>
|
||||
</div>
|
||||
</section>
|
||||
</div>
|
||||
</div>
|
||||
);
|
||||
};
|
||||
|
||||
export default CirclePropertiesLesson;
|
||||
Reference in New Issue
Block a user