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Iran geometry

Source: Iran MO 3rd round 2017 mid-terms - Geometry P1

August 10, 2017
geometrycircumcircleincenter

Problem Statement

Let ABCABC be a triangle. Suppose that X,YX,Y are points in the plane such that BX,CYBX,CY are tangent to the circumcircle of ABCABC, AB=BX,AC=CYAB=BX,AC=CY and X,Y,AX,Y,A are in the same side of BCBC. If II be the incenter of ABCABC prove that ∠BAC+∠XIY=180\angle BAC+\angle XIY=180.
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