Problem

Source: Taiwan 3rd TST 2005, 3rd independent study, problem 2

Tags: geometry proposed, geometry



Given a triangle ABC, A1 divides the length of the path CAB into two equal parts, and define B1 and C1 analogously. Let lA, lB, lC be the lines passing through A1, B1 and C1 and being parallel to the bisectors of A, B, and C. Show that lA, lB, lC are concurrent.