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In right triangle ABC, AC = BC and angle C = 90. Let P and Q be points on hypotenuse AB, as shown below, such that angle PCQ=45. Show that AP^2 + BQ^2 = PQ^2. I think the first step is to rotate it 90 degrees counter clockwise around C, let P go to P’ and find angle P’CQ

 Oct 25, 2020
edited by Guest  Oct 25, 2020
 #1
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This is trivial by the Cosine Law.  Try applying it to triangle CPQ.

 Oct 25, 2020
 #2
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Hint:          If   AP = BQ     then    PQ = 2 * [tan(22.5º) * AB/2]

 Oct 25, 2020

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