MathDB
arc midpoint equidistant from incenters (V Soros Olympiad 1998-99 Round 3 9.7)

Source:

May 25, 2024
geometryincenter

Problem Statement

Consider the cyclic quadrilateral ABCDABCD. Let MM be the point of intersection of its diagonals, and LL be the midpoint of the arc ADAD (not containing other vertices of the quadrilateral). Prove that the distances from LL to the centers of the circles inscribed in triangles ABMABM and CDMCDM are equal.