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Isogonal conjugates

Source: Romania TST 2015 Day 1 Problem 1

April 9, 2015
Isogonal conjugateorthocenterCircumcentergeometry

Problem Statement

Let ABCABC be a triangle, let OO be its circumcenter, let A′A' be the orthogonal projection of AA on the line BCBC, and let XX be a point on the open ray AA′AA' emanating from AA. The internal bisectrix of the angle BACBAC meets the circumcircle of ABCABC again at DD. Let MM be the midpoint of the segment DXDX. The line through OO and parallel to the line ADAD meets the line DXDX at NN. Prove that the angles BAMBAM and CANCAN are equal.
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