Symmetric points and intersecting lines

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.

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