NOTE: Because of the upcoming Spring Break this problem will stand for the next two weeks. 

Consider a yard in the shape of an equilateral triangle with sides of length 1.  At each of the corners of the yard stand tall poles of heights a, b, and c, respectively .  What is the location of the point P in the yard from which wires, each of length L, can be run to the top of the poles?  See the figure on the left.