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TOT 110 1986 Spring J4 intersection of circumcircles lies on square's diagonal

Source:

August 29, 2019
geometrycircumcirclesquarediagonal

Problem Statement

We are given the square ABCDABCD. On sides ABAB and CDCD we are given points K K and LL respectively, and on segment KLKL we are given point MM . Prove that the second intersection point (i.e. the one other than MM) of the intersection points of circles circumscribed around triangles AKMAKM and MLCMLC lies on the diagonal ACAC.
(V . N . Dubrovskiy)
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