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Going to the third power

Source: Indonesian Mathematical Olympiad 2014 Day 2 Problem 6

September 4, 2014
geometrycircumcirclegeometry unsolved

Problem Statement

Let ABCABC be a triangle. Suppose DD is on BCBC such that ADAD bisects ∠BAC\angle BAC. Suppose MM is on ABAB such that ∠MDA=∠ABC\angle MDA = \angle ABC, and NN is on ACAC such that ∠NDA=∠ACB\angle NDA = \angle ACB. If ADAD and MNMN intersect on PP, prove that AD3=AB⋅AC⋅APAD^3 = AB \cdot AC \cdot AP.
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