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Congruent triangles

Source: MEMO 2009, problem 5, team competition

October 1, 2009
geometryparallelogramcircumcirclegeometry proposed

Problem Statement

Let ABCD ABCD be a parallelogram with \angle BAD \equal{} 60 and denote by E E the intersection of its diagonals. The circumcircle of triangle ACD ACD meets the line BA BA at K≠A K \ne A, the line BD BD at P≠D P \ne D and the line BC BC at L≠C L\ne C. The line EP EP intersects the circumcircle of triangle CEL CEL at points E E and M M. Prove that triangles KLM KLM and CAP CAP are congruent.
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