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starting with a right triangle, angles between two lines wanted

Source: May Olympiad (Olimpiada de Mayo) 2011 L2

September 11, 2018
geometryright triangleisoscelesangleperpendicular bisector

Problem Statement

In a right triangle rectangle ABCABC such that AB=ACAB = AC, MM is the midpoint of BCBC. Let PP be a point on the perpendicular bisector of ACAC, lying in the semi-plane determined by BCBC that does not contain AA. Lines CPCP and AMAM intersect at QQ. Calculate the angles that form the lines APAP and BQBQ.
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