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Symmedian and circumcircles

Source: Baltic Way 2004 Problem 19

November 19, 2004
geometrycircumcirclegeometric transformationreflectionratioangle bisectorgeometry proposed

Problem Statement

Let DD be the midpoint of the side BCBC of a triangle ABCABC. Let MM be a point on the side BCBC such that ∠BAM=∠DAC\angle BAM = \angle DAC. Further, let LL be the second intersection point of the circumcircle of the triangle CAMCAM with the side ABAB, and let KK be the second intersection point of the circumcircle of the triangle BAMBAM with the side ACAC. Prove that KL∥BCKL \parallel BC.
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