formula for finding the sides of a triangle code example

Example: how to find a point on a triangle with only sides

known sides AB, BC, AC
known points A(x, y), B(x, y)
unknown points C(x, y)

AC² - BC² = ((Ax - Cx)² + (Ay - Cy)²) - ((Bx - Cx)² + (By - Cy)²)


Goal: 

C.x = ?
C.y = ?