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Sharygin CR 2019 P16

Source: Sharygin CR 2019 P16 (Grade 9 - 11)

March 6, 2019
geometry

Problem Statement

Let AH1AH_1 and BH2BH_2 be the altitudes of triangle ABCABC. Let the tangent to the circumcircle of ABCABC at AA meet BCBC at point S1S_1, and the tangent at BB meet ACAC at point S2S_2. Let T1T_1 and T2T_2 be the midpoints of AS1AS_1 and BS2BS_2 respectively. Prove that T1T2T_1T_2, ABAB and H1H2H_1H_2 concur.
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