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4 points concyclic, symmedian and altitudes involved

Source: Sharygin Geometry Olympiad 2016 First Round P12 grades 9-10

July 25, 2018
geometryConcyclicsymmedian

Problem Statement

Let BB1BB_1 be the symmedian of a nonisosceles acute-angled triangle ABCABC. Ray BB1BB_1 meets the circumcircle of ABCABC for the second time at point LL. Let AHA,BHB,CHCAH_A, BH_B, CH_C be the altitudes of triangle ABCABC. Ray BHBBH_B meets the circumcircle of ABCABC for the second time at point TT. Prove that HA,HC,T,LH_A, H_C, T, L are concyclic.
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