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# Help Geometry

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

$$[asy] unitsize(3 cm); pair A, B, C, P, Q; A = (1,0); B = (0,1); C = (0,0); P = extension(C, C + dir(16), A, B); Q = extension(C, C + dir(16 + 45), A, B); draw(A--B--C--cycle); draw(C--P); draw(C--Q); label("A", A, SE); label("B", B, NW); label("C", C, SW); label("P", P, NE); label("Q", Q, NE); [/asy]$$

off-topic
Feb 16, 2020
edited by Guest  Feb 16, 2020