MathDB
Circumcenter on BC, Angle Bisectors

Source: 2022 Israel TST 8 P3

May 21, 2022
geometrycircumcircleIMO 2022 tstangle bisectorcircles

Problem Statement

In triangle ABCABC, the angle bisectors are BEBE and CFCF (where E,FE, F are on the sides of the triangle), and their intersection point is II. Point NN lies on the circumcircle of AEFAEF, and the angle IAN\angle IAN is right. The circumcircle of AEFAEF meets the line NINI a second time at the point LL. Show that the circumcenter of AILAIL lies on line BCBC.