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equal angles wanted, circumcircle and angle bisector related

Source: Ukraine TST 2015 p1

May 1, 2020
geometryangle bisectorequal anglescircumcircle

Problem Statement

Let OO be the circumcenter of the triangle ABC,A′ABC, A' be a point symmetric of AA wrt line BC,XBC, X is an arbitrary point on the ray AA′AA' (X≠AX \ne A). Angle bisector of angle BACBAC intersects the circumcircle of triangle ABCABC at point DD (D≠AD \ne A). Let MM be the midpoint of the segment DXDX. A line passing through point OO parallel to ADAD, intersects DXDX at point NN. Prove that angles BAMBAM and CANCAN angles are equal.
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