Problem

Source: Romanian TST 2011

Tags: geometry, incenter, search, geometry proposed



The incircle of a triangle ABC touches the sides BC,CA,AB at points D,E,F, respectively. Let X be a point on the incircle, different from the points D,E,F. The lines XD and EF,XE and FD,XF and DE meet at points J,K,L, respectively. Let further M,N,P be points on the sides BC,CA,AB, respectively, such that the lines AM,BN,CP are concurrent. Prove that the lines JM,KN and LP are concurrent. Dinu Serbanescu