Right-angled Request

'Right-angled Request' printed from https://nrich.maths.org/

The figure shows a rectangle PRSU with a line QT, which divides the rectangle into two squares.

How many right-angle triangles can be drawn using any three points P, Q, R, S, T, U as corners?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.