MathDB
Polish MO Finals 2018, Problem 1

Source:

April 18, 2018
geometryPolandgeometry solvedradical axisAngle Chasing

Problem Statement

An acute triangle ABCABC in which AB<ACAB<AC is given. The bisector of BAC\angle BAC crosses BCBC at DD. Point MM is the midpoint of BCBC. Prove that the line though centers of circles escribed on triangles ABCABC and ADMADM is parallel to ADAD.