MathDB

2

Part of 2017 German National Olympiad

Problems(1)

Two circumcircles intersecting in a fixed point

Source: Germany 2017, Problem 2

5/4/2017
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.
geometrycircumcircleFixed pointGermanygeometry proposed