IMO 1983 LL NET47

In a plane, three pairwise intersecting circles C1, C2, C3 with

imolonglistmathematicsolympiad

IMO 1983 LL NET47

Origin: NET

Problem

In a plane, three pairwise intersecting circles C1, C2, C3 with centers M1, M2, M3 are given. For i = 1, 2, 3, let Ai be one of the points of intersection of Cj and Ck ({i, j, k} = {1, 2, 3}). Prove that if \angleM3A1M2 = \angleM1A2M3 = \angleM2A3M1 = \pi/3 (directed angles), then M1A1, M2A2, and M3A3 are concurrent.