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Iran geometry

Source: Iran MO 3rd round 2019 finals - Geometry P1

August 14, 2019
geometryincentercircumcirclegeometric transformationreflectionLaw of SinesMenelaus

Problem Statement

Consider a triangle ABCABC with incenter II. Let DD be the intersection of BI,ACBI,AC and CICI intersects the circumcircle of ABCABC at MM. Point KK lies on the line MDMD and ∠KIA=90∘\angle KIA=90^\circ. Let FF be the reflection of BB about CC. Prove that BIKFBIKF is cyclic.
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