line of 2 incenters perpendicular to angle bisector
Source: All-Russian MO 2002 Regional (R4) 10.3
September 17, 2024
geometryincenterperpendicularangle bisector
Problem Statement
The perpendicular bisector to side of triangle intersects side at point (see fig.). The bisector of angle intersects the circumcircle of triangle at point . Prove that the line passing through the centers of the inscribed circles triangles and , perpendicular to the bisector of angle .
https://cdn.artofproblemsolving.com/attachments/b/4/b53ec7df0643a90b835f142d99c417a2a1dd45.png