MathDB
AX is independent of the choice of P, XI_1 _|_ XI_2, 2 incenters

Source: Switzerland - 2022 Swiss Final Round p8

November 17, 2022
geometryincenterfixed

Problem Statement

Let ABCABC be a triangle and let PP be a point in the interior of the side BCBC. Let I1I_1 and I2I_2 be the incenters of the triangles APBAP B and APCAP C, respectively. Let XX be the closest point to AA on the line APAP such that XI1XI_1 is perpendicular to XI2XI_2. Prove that the distance AXAX is independent of the choice of PP.
Back to ProblemsView on AoPS