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Math Help - An Area property of Triangles

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    An Area property of Triangles

    Let P be a point inside triangle \Delta ABC, and lines through \{A,P\},\{B,P\},\{C,P\}
    intersect the sides of \Delta ABC at A_1, B_1, C_1. Let A_2, B_2, C_2 be the symmetric points of
    P on segments \overline{AA}_1, \overline{BB}_1, \overline{CC}_1 with respect to their middle points A_m,B_m, C_m

    Show that |\Delta A_1 B_1 C_1| = |\Delta A_2 B_2 C_2|
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