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congruent triangles wanted, # with 60^o

Source: Mathematics Regional Olympiad of Mexico Center Zone 2012 P3

November 8, 2021
geometryparallelogramcongruent triangles

Problem Statement

In the parallelogram ABCDABCD, BAD=60\angle BAD =60 ^ \circ. Let EE be the intersection point of the diagonals. The circle circumscribed to the triangle ACDACD intersects the line ABAB at the point KK (different from AA), the line BDBD at the point PP (different from DD), and to the line BCBC in LL (different from CC). The line EPEP intersects the circumscribed circle of the triangle CELCEL at the points EE and MM. Show that the triangles KLMKLM and CAPCAP are congruent.