Can you solve this tricky RED area? | Finland math competition

Master this geometry problem involving a square with an area of 180 and a chord length of 8 to find the area of the red semicircle. This breakdown covers the precise steps required to solve for a semicircle's area using geometric principles. If you are preparing for math competitions or reviewing high school geometry, this walkthrough provides the exact algebraic steps needed to navigate complex figures. We apply Euclid's Cathetus Theorem and the Inscribed Angle Theorem to break down the relationship between the square and the semicircle, ensuring you understand the logic behind each step. By following this geometric figure analysis, you will learn how to set up quadratic equations from geometric constraints. We strip away the complexity, showing you how to manipulate the variables to reach the final measurement for the area of the red semicircle. This method focuses on clear, logical progression rather than guessing. 📌 Chapters: 0:00 Presenting the puzzle 1:16 Inscribed Angle Theorem 3:07 Euclid's Cathetus Theorem 5:22 Method of splitting the middle term Subscribe for weekly math problem breakdowns, and let me know in the comments if you want to see more geometry proofs like this. Join the Chanel 👉    / @thephantomofthemath   -------------------------------------------------------------- 📧 Contact Me: ✉️ [email protected] -------------------------------------------------------------- Music by Helkimer - original - https://thmatc.co/?l=211EE660 Get vidIQ to grow your channel faster! 🚀 https://vidiq.com/ThePhantomoftheM