This took a while (15 mins), but appealing to the fact that for ANY similar shapes drawn on the sides of a right angled triangle the result comes out in one line. Nice!

Nice use of Pythagorean theorem: the surface of the half disk with the hypotenuse as its diameter is the sum of the areas of the half disks having the two other sides as their diameters. The result easily follows.

This took a while (15 mins), but appealing to the fact that for ANY similar shapes drawn on the sides of a right angled triangle the result comes out in one line. Nice!

Love it. Not tried to solve it yet but looks good! Really cool style of problem for discussion with pupils, thanks.

Is there a solution anywhere? Feeling a little 😦

Here’s 1 solution

thanks for sharing. I would have never thought of that 🙂

Nice use of Pythagorean theorem: the surface of the half disk with the hypotenuse as its diameter is the sum of the areas of the half disks having the two other sides as their diameters. The result easily follows.