# Thread: An Area property of Triangles

1. ## 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 $|\Delta A_1 B_1 C_1| = |\Delta A_2 B_2 C_2|$