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İncircle

Source: Balkan MO 2012 Shortlist G5

May 15, 2016
geometry

Problem Statement

G5\boxed{\text{G5}} The incircle of a triangle ABCABC touches its sides BCBC,CACA,ABAB at the points A1A_1,B1B_1,C1C_1.Let the projections of the orthocenter H1H_1 of the triangle A1B1C1A_{1}B_{1}C_{1} to the lines AA1AA_1 and BCBC be PP and QQ,respectively. Show that PQPQ bisects the line segment B1C1B_{1}C_{1}
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