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Concurrent

Source: Tuymaada 2016, Seniors/P3

July 22, 2016
geometry

Problem Statement

Altitudes AA1AA_1, BB1BB_1, CC1CC_1 of an acute triangle ABCABC meet at HH. A0A_0, B0B_0, C0C_0 are the midpoints of BCBC, CACA, ABAB respectively. Points A2A_2, B2B_2, C2C_2 on the segments AHAH, BHBH, HC1HC_1 respectively are such that ∠A0B2A2=∠B0C2B2=∠C0A2C2=90∘\angle A_0B_2A_2 = \angle B_0C_2B_2 = \angle C_0A_2C_2 =90^\circ. Prove that the lines AC2AC_2, BA2BA_2, CB2CB_2 are concurrent.
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