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In right triangle \(ABC,\)  \(AC=BC\) and \(\angle C = 90^\circ.\) Let \(P\) and \(Q\) be points on hypotenuse \(\overline{AB},\) as shown below, such that \(\angle PCQ = 45^\circ.\) Show that \(AP^2 + BQ^2 = PQ^2.\)

 

 

Thank you very much!

 May 8, 2020
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here's a hint: reflect the triangle around C so that AC is on BC and look for similar triangles

 

i'll write out a whole solution in a bit but that's mainly what you need to figure it out

 May 8, 2020
edited by chrissy  May 8, 2020

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