MathDB
orthocenter and collinear wanted, incircle, circumcircle related

Source: 2016 Saudi Arabia IMO TST , level 4, IV p1

July 27, 2020
geometrycircumcircleincircleorthocentercollinear

Problem Statement

Let ABCABC be a triangle whose incircle (I)(I) touches BC,CA,ABBC, CA, AB at D,E,FD, E, F, respectively. The line passing through AA and parallel to BCBC cuts DE,DFDE, DF at M,NM, N, respectively. The circumcircle of triangle DMNDMN cuts (I)(I) again at LL. a) Let KK be the intersection of NEN E and MFM F. Prove that KK is the orthocenter of the triangle DMNDMN. b) Prove that A,K,LA, K, L are collinear.
Back to ProblemsView on AoPS