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Two circumcircles intersecting in a fixed point

Source: Germany 2017, Problem 2

May 4, 2017
geometrycircumcircleFixed pointGermanygeometry proposed

Problem Statement

Let ABCABC be a triangle such that ∣AB∣≠∣AC∣\vert AB\vert \ne \vert AC\vert. Prove that there exists a point D≠AD \ne A on its circumcircle satisfying the following property: For any points M,NM, N outside the circumcircle on the rays ABAB and ACAC, respectively, satisfying ∣BM∣=∣CN∣\vert BM\vert=\vert CN\vert, the circumcircle of AMNAMN passes through DD.
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