A simple geometry puzzle

I found a fun puzzle last week, which I would like to share with you. It concerns the following figure.

the puzzle

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?


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

Hint 2

Hint 3

Hint 4