Unraveling the Angle in a Triangle: A Geometry Challenge
Written on
Chapter 1: Understanding the Puzzle
Recently, I received an intriguing geometry challenge from Llorenc Sole, inspired by Catriona. This puzzle presents a unique scenario: a triangle situated within a circle, which itself is contained within a triangle that lies in a semi-circle.
Can you determine the missing angle marked with a question mark? I suggest you take a moment to think it through with some paper and a pencil. Once you're ready, continue reading for the solution!
Solution
This puzzle isn’t overly complicated if you recall your circle theorems! We’ll begin by examining the larger triangle along with the semi-circle.
In this scenario, the hypotenuse of the triangle matches the radius of the semi-circle. According to the properties of circles, any angle formed along the semi-circle's arc is always a right angle, measuring 90 degrees.
With this in mind, we can create a quadrilateral:
Pardon my drawing skills—I'm still learning! By connecting the two radii from the tangential points, a right angle is established at the circle's center. Another circle theorem states that the angle at the circumference is half of the angle at the center.
Thus, 90 degrees divided by 2 gives us 45 degrees! And there’s your answer.
Isn’t that fascinating?
What was your reasoning process for this puzzle? Please share your thoughts in the comments—I’d love to hear from you!
Video Description: This video titled "Angles in a triangle" breaks down the principles of angles within triangles, providing additional insights and examples.
Video Description: In the second video, "Angles In a Triangle," viewers can explore various concepts related to triangle angles and their properties.
Chapter 2: Engaging with Math
Math Puzzles
Looking for more challenging math puzzles? Check out the best math puzzles on Medium, featuring topics like Algebra, Geometry, Calculus, and Number Theory. Share these with your friends!
Bella’s Weekly Math Games
Join us for a weekly 48-hour math competition! Test your skills and challenge yourself against others.
The Mathsy Way
Understanding math concepts made easy.
Thank you for taking the time to read this article. If you found it helpful, please consider giving it a clap!
If you'd like to support my writing, consider buying me a coffee! Your generosity means a lot and helps me continue creating quality content. Happy solving!