I found a fun puzzle last week, which I would like to share with you. It concerns the following figure.
You are given a right-angled circle sector, with a square inscribed. Beside the square another square is inscribed. The question for you is: how big are the squares? To make things easier, let's say the circle has a radius of \(\sqrt{250}\). What, then, are the side lengths of the inscribed squares?
Hints
In case your geometry skills are a bit rusty, I have prepared a series of hints you may find helpful. To avoid giving it all away, I will hide them until you click the button to reveal them.
Hint 1
When you are given a point on the arc of a circle, it is often helpful to draw a line connecting that point to the circle center.
Hint 2
The Pythagorean theorem is your friend. Look for ways to make right triangles.
Hint 3
Hint 4
