This math problem from Colin Hughes’s Maths Challenge website (mathschallenge.net) is a bit more challenging.
“In the diagram, AB represents the diameter, C lies on the circumference of the circle, and you are given that
(Area of Circle) / (Area of Triangle) = 2π.
Prove that the two smaller angles in the triangle are exactly 15° and 75° respectively.”
See the 15 Degree Triangle Puzzle