Symmetric points and intersecting lines

Submitted by Structure on Mon, 11/19/2007 - 18:28.

Let ABC be a triangle and D a point in its plan. Let $A_1,B_1,C_1$ be the middle of $BC, CA$ and $AB$ . Let $A_2,B_2,C_2$ be the symmetric points of $D$ with respect to $A_1,B_1,C_1$ . Then the lines $AA_2, BB_2,$ and $CC_2$ intersect.