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!
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
