MathDB

3

Part of 2016 German National Olympiad

Problems(1)

Parallel lines involving the A-excenter

Source: Germany 2016 - Problem 3

6/19/2016
Let IaI_a be the AA-excenter of a scalene triangle ABCABC. And let MM be the point symmetric to IaI_a about line BCBC. Prove that line AMAM is parallel to the line through the circumcenter and the orthocenter of triangle IaCBI_aCB.
geometrycircumcircleexcenterparallelorthocenter