Tangency of the Red Circle:
Tangency of the Green Circle:
Tangency of the Blue Circle:

ⓘ This interactive app demonstrates an algorithm that finds a circle (gray) that is tangent to, or touching, three known circles (red, green, blue). You can drag the known circles around using the mouse or touch. The result is one of the eight solutions to the Problem of Apollonius. The algorithm can be used for circle packing, node-link graph layouts, and data visualization in general.

See more at github.com/axelpale/apollonius.