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A, I and T are collinear iff [BKS]=[CKR]

Source: Chinese Mathematical Olympiad 2003 Problem 1

February 18, 2012
geometryincentercircumcirclegeometry proposed

Problem Statement

Let II and HH be the incentre and orthocentre of triangle ABCABC respectively. Let P,QP,Q be the midpoints of AB,ACAB,AC. The rays PI,QIPI,QI intersect AC,ABAC,AB at R,SR,S respectively. Suppose that TT is the circumcentre of triangle BHCBHC. Let RSRS intersect BCBC at KK. Prove that A,IA,I and TT are collinear if and only if [BKS]=[CKR][BKS]=[CKR].
Shen Wunxuan
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