MathDB
Incenter geo

Source: BMO Shortlist 2022, G2

May 13, 2023
geometryAZE EGMO TSTAZE BMO TST

Problem Statement

Let ABCABC be a triangle with AB>ACAB > AC with incenter II{}. The internal bisector of the angle BACBAC intersects the BCBC at the point DD{}. Let MM{} the midpoint of the segment ADAD{}, and let FF{} be the second intersection point of MBMB with the circumcircle of the triangle BICBIC. Prove that AFAF is perpendicular to FCFC.
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