MathDB
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 ACAC of triangle ABCABC intersects side BCBC at point MM (see fig.). The bisector of angle AMB\angle AMB intersects the circumcircle of triangle ABCABC at point KK. Prove that the line passing through the centers of the inscribed circles triangles AKMAKM and BKMBKM, perpendicular to the bisector of angle AKB\angle AKB. https://cdn.artofproblemsolving.com/attachments/b/4/b53ec7df0643a90b835f142d99c417a2a1dd45.png