MathDB

P12

Part of 2016 Sharygin Geometry Olympiad

Problems(1)

4 points concyclic, symmedian and altitudes involved

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

7/25/2018
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.
geometryConcyclicsymmedian