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find angle in circle and triangle configuration (Serbia MO 2005 1st Grade P2)

Source:

April 11, 2021
geometry

Problem Statement

Let ABCABC be an acute triangle. Circle kk with diameter ABAB intersects ACAC and BCBC again at MM and NN respectively. The tangents to kk at MM and NN meet at point PP. Given that CP=MNCP=MN, determine ∠ACB\angle ACB.
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