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Iran NMO 2007 (Second Round) - Problem1

Source:

September 22, 2010
geometrycircumcirclegeometry proposed

Problem Statement

In triangle ABCABC, ∠A=90∘\angle A=90^{\circ} and MM is the midpoint of BCBC. Point DD is chosen on segment ACAC such that AM=ADAM=AD and PP is the second meet point of the circumcircles of triangles ΔAMC,ΔBDC\Delta AMC,\Delta BDC. Prove that the line CPCP bisects ∠ACB\angle ACB.
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