Circle of Apollonius
A circle of Apollonius is defined by a circle which passes through a vertex on a triangle, where the two adjacent sides, when divided, remain the same no matter where point the point lies on the triangle. This means that if triangle ABC is on the coordinate plane and a circle passes through point C, the length of side AC divided by the length of side BC would remain constant if point C were to move across the border of the circle. This means that a triangle with points (-8,0) and (-2,0) with a circle with center on (0,0) and a radius of 4 the ratio of the side lengths is 2:1 and remains the same all around the circle wherever point C is placed on it.