2 Genius Methods to Find the Area of the Rectangle

Can you find the area of this rectangle? 📐 In today's video, we tackle a fascinating geometry puzzle involving a rectangle, a quarter circle, and a semicircle. While it might look complex at first, we’ll show you how to solve it using two completely different—and equally genius—methods! The Challenge: We have a rectangle ABCD with a quarter circle tucked inside and a semicircle attached below. Given that the tangent segment BQ is exactly 9 units long, what is the total area of the rectangle? What you’ll learn in this video: Method 1: The Algebraic Approach – We’ll use the Pythagorean theorem to break down the relationship between the radii and the rectangle's dimensions. Method 2: The Geometric Shortcut – Discover how the Power of a Point theorem (Tangent-Secant Theorem) can provide a lightning-fast solution. Whether you're a student looking to sharpen your geometry skills or a math enthusiast who loves a good challenge, this video has something for you. Timestamps: 0:00 - The Problem Setup 0:28 - Setting up the Variables 1:54 - Method 1: Pythagorean Theorem 3:37 - Method 2: Tangent-Secant Theorem 4:50 - Final Answer & Wrap-up Join the Conversation: Which method did you find first? Or did you discover a third way to solve it? Let us know in the comments below! 👇 If you enjoyed this logic booster, don't forget to: ✅ Like the video ✅ Subscribe for more math challenges ✅ Share with a friend who loves puzzles #Geometry #MathPuzzles #LogicBooster #Mathematics #ProblemSolving #Education