Problem #PRU-5167

Problem

Consider a triangle $CDE$. The lines $CD$, $DE$, and $CE$ are tangent to a circle with centre $A$ at the points $F,G$, and $B$ respectively. We also have that the angle $\mathrm{\angle }DCE={120}^{\circ }$. Prove that the length of the segment $AC$ equals the perimeter of the triangle $CDE$.