Start with any cyclic quadrilateral. Draw one of the diagonals and inscribe red circles in the resulting triangles. Then repeat for the other diagonal, creating two blue circles.

The Japanese theorem for quadrilaterals: The sum of the radii of the red circles equals the sum of the radii of the blue circles.

(Neat fact: the centers of the four circles form a rectangle.)

The circle shown below has radius 1. Slide the points around the circle without changing their order.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Created by Dave Richeson using GeoGebra.