Circle of Apollonius
The Circle of Apollonius is associated with the Greek geometer Apollonius of Perga. The one thing that separates a Circle of Apollonius from a regular circle is that an Apollonian Circle could be defined as a set of points ( labeled E in the diagram) that have a given ratio of distances to two given points (labeled A and B in the diagram), also known as the foci. A Circle of Apollonius can be created through the vertex of any triangle.
Point Glossary:
A, B, and C - the original points of the triangle
D - Point of intersection between angle bisector ∠ACB and base of triangle
F - Point on ray BC and is used to create the angle bisector ∠FCA
G - Point of Intersection between angle bisector ∠FCA and base of triangle.
H - Center of the Cirlce of Apollonius
E - Point that traces out the locus