MathDB

20

Part of 2023 Sharygin Geometry Olympiad

Problems(1)

line joining isogonals parallel to line through tangents

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

3/4/2023
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.
geometryIsogonal conjugatetangentsymmedianParallel LinesSharygin Geometry OlympiadSharygin 2023