MathDB
Three circles meet at a point

Source: Own. Malaysian IMO TST 2023 P3

April 29, 2023
geometry

Problem Statement

Let ABCABC be an acute triangle with AB≠ACAB\neq AC. Let D,E,FD, E, F be the midpoints of the sides BCBC, CACA, and ABAB respectively, and M,NM, N be the midpoints of minor arc BCBC not containing AA and major arc BACBAC respectively. Suppose W,X,Y,ZW, X, Y, Z are the incenter, DD-excenter, EE-excenter, and FF-excenter of triangle DEFDEF respectively.
Prove that the circumcircles of the triangles ABCABC, WNXWNX, YMZYMZ meet at a common point.
Proposed by Ivan Chan Kai Chin
Back to ProblemsView on AoPS