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bisector of XAY - Iran NMO 2004 (Second Round) - Problem5

Source:

September 24, 2010
geometrycircumcircleincentergeometry solvedpower of a pointInversionIranMO

Problem Statement

The interior bisector of ∠A\angle A from △ABC\triangle ABC intersects the side BCBC and the circumcircle of ΔABC\Delta ABC at D,MD,M, respectively. Let ω\omega be a circle with center MM and radius MBMB. A line passing through DD, intersects ω\omega at X,YX,Y. Prove that ADAD bisects ∠XAY\angle XAY.
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