MathDB
Problem 5

Source: Paraguayan Mathematical Olympiad 2013

July 25, 2015
geometry

Problem Statement

Let ABCABC be an obtuse triangle, with ABAB being the largest side. Draw the angle bisector of ∡BAC\measuredangle BAC. Then, draw the perpendiculars to this angle bisector from vertices BB and CC, and call their feet PP and QQ, respectively. DD is the point in the line BCBC such that AD⊥APAD \perp AP. Prove that the lines ADAD, BQBQ and PCPC are concurrent.
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