Can You Find the Semicircle Area?

Can you find the exact area of the green semicircle? 📐 In this video, we dive into a beautiful geometry puzzle involving a large right triangle ABC and a semicircle tucked perfectly inside it. We are given that the semicircle is tangent to the hypotenuse AB, splitting it into segments of length 8 and 9. Using the properties of tangents from an external point, the Pythagorean theorem, and triangle similarity, we’ll walk through the step-by-step solution to find the radius and the final area. In this video, you will learn: How to apply the tangent segments theorem. How to use similar triangles to solve for unknown variables. The step-by-step calculation for the area of a semicircle. Did you find a different way to solve this? Let me know your method in the comments below! Subscribe to Logic Booster for more math challenges and geometry puzzles!