Cute geometry with bisectors and tangential circumcircles
Source: Turkey National Mathematical Olympiad 2022 P1
December 23, 2022
geometrygeometry proposedcircumcircle
Problem Statement
In triangle , is the midpoint of side , the bisector of angle intersects and at and , respectively. If the circle with diameter is tangent to the external angle bisector of angle , prove that this circle is tangent to as well.