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Another geometry

Source: St Petersburg Olympiad 2014, Grade 11, P7

October 24, 2017
geometryincentercircumcircleangle bisector

Problem Statement

II - incenter , MM- midpoint of arc BACBAC of circumcircle, ALAL - angle bisector of triangle ABCABC. MIMI intersect circumcircle in KK. Circumcircle of AKLAKL intersect BCBC at LL and PP. Prove that ∠AIP=90\angle AIP=90
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