Hello, in a pre-calculus book I am given this problem:

Find the coordinates of the point of intersection of the perpendicular bisectors of the sides of a triangle whose vertices are located at (-a, 0), (b, c), and (a, 0).The only apparent tools with which we are supposed to find the answer are the Pythagorean theorem, the distance formula, the midpoint formula, and the equation of a line.

I have tried this a couple of times but end up drowned in variables. Could anyone give me a hand?