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line joining isogonals parallel to line through tangents

Source: Sharygin 2023 - P20 (Grade-10-11)

March 4, 2023
geometryIsogonal conjugatetangentsymmedianParallel LinesSharygin Geometry OlympiadSharygin 2023

Problem Statement

Let a point DD lie on the median AMAM of a triangle ABCABC. The tangents to the circumcircle of triangle BDCBDC at points BB and CC meet at point KK. Prove that DD′DD' is parallel to AKAK, where D′D' is isogonally conjugated to DD with respect to ABCABC.
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