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In a triangle ABC whose angle A is a right angle. Let Q denote the point where the bisector r of the angle A meets BC, and let P be the point where the line through B and perpendicular to r intersects AC.

Let ABC be a right-angled triangle at A with altitude AH and M as the midpoint of BC. a) Find the measure of ∠ABC when ∠MAC = ∠HAM.