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'Weekly Problem 26 - 2006' printed from http://nrich.maths.org/

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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.

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