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Geometry problem from Nordic MO 2012

Source: Nordic MO 2012 Q2

April 21, 2013
geometrycircumcirclegeometric transformationreflectiongeometry unsolved

Problem Statement

Given a triangle ABCABC, let PP lie on the circumcircle of the triangle and be the midpoint of the arc BCBC which does not contain AA. Draw a straight line ll through PP so that ll is parallel to ABAB. Denote by kk the circle which passes through BB, and is tangent to ll at the point PP. Let QQ be the second point of intersection of kk and the line ABAB (if there is no second point of intersection, choose Q=BQ = B). Prove that AQ=ACAQ = AC.
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