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concurrency of lines formed by perpendiculars

Source: Ukraine 1999 Grade 10 P8

May 11, 2021
geometryTriangles

Problem Statement

Let AA1,BB1,CC1AA_1,BB_1,CC_1 be the altitudes of an acute-angled triangle ABCABC, and let OO be an arbitrary interior point. Let M,N,P,Q,R,SM,N,P,Q,R,S be the feet of the perpendiculars from OO to the lines AA1,BC,BB1,CA,CC1,ABAA_1,BC,BB_1,CA,CC_1,AB, respectively. Prove that the lines MN,PQ,RSMN,PQ,RS are concurrent.
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