The Seven Circles Theorem

disk radii

red

0.33

blue

0.33

green

0.33

move disk

blue

2.1

green

4.2

Take six circles tangent to each other in pairs and tangent to the unit circle on the inside. The points of contact of the six circles with the unit circle define a hexagon. The diagonals of the hexagon are concurrent.

This concurrency is obvious when the hexagon is regular. The theorem states that it still holds when the radii and the positions of the circles vary.