Given a triangle ABC and a point K . The lines AK,BK,CK hit the opposite side of the triangle at D,E,F respectively. On the exterior of ABC, we construct three pairs of similar triangles: BDM,DCN on BD,DC, CEP,EAQ on CE,EA, and AFR,FBS on AF, FB. The lines MN,PQ,RS intersect each other form a triangle XYZ. Prove that AX,BY,CZ are concurrent. geometrysimilar trianglesconcurrencyconcurrent