Google Classroom
GeoGebraGeoGebra Classroom

Circles of Apollonius

The Greek mathematician Apollonius (c. 200 BC) proved that for any three circles with no common points or common interiors, there are eight ways to draw a circle that is tangent to the three given circles. Shown are two examples. Notice that the colored circles have not moved, but that the "clear" circle has been moved so that it is tangent to all three colored circles. In each of the diagrams below, your job is to move the "clear" circle so that it is tangent to the three colored circles. You need to do this in 8 unique ways, which is why there are 8 diagrams to complete.