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Let WXYZ be a square. Let P be a point inside the square, so that triangle PWX is right isosceles. Compute \angle PYZ.

 
 Jan 4, 2025

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The only possible way P can exist inside square WXYZ so that triangle PWX is a right isosceles is in the center of the square. Therefore, triangle PZY is 1/4th the square, and PY is part of the diagonal, so angle PYZ is 45 degrees.
 Jan 5, 2025

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