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TOT 2006 Fall - Senior A-Level p2 altitudes wanted

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February 25, 2020
altitudegeometry

Problem Statement

Suppose ABCABC is an acute triangle. Points A1,B1A_1, B_1 and C1C_1 are chosen on sides BC,ACBC, AC and ABAB respectively so that the rays A1A,B1BA_1A, B_1B and C1CC_1C are bisectors of triangle A1B1C1A_1B_1C_1. Prove that AA1,BB1AA_1, BB_1 and CC1CC_1 are altitudes of triangle ABCABC. (6)
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