Let ABC be a right triangle with B the right angle. X,Y and Z are on BC, CA and AB respectively such that BXYZ is a square. If the square is of side length m, AY = r and YC = s, find m in terms of r and s.
I have two solutions for my students (I instruct a math team class): One involves proportions and the other involves the angle bisector theorem (BY is an angle bisector). I am just curious of there are any other creative solutions for this problem.