Soddy circles are named after Frederick Soddy, who in 1936. He proved that given three circles that are tangent to the other two, exactly two circles can be drawn that are tangent to all three; one very big circle, and one very small circle. I used Geogebra to draw these circles. The three red circles are all tangent to each other. The big, blue circle is tangent to all three at the points P, M, and O. It is called the outer Soddy circle and its centre, R, is called the outer Soddy centre. The smaller blue circle that is in the middle is called the inner Soddy circle, and its centre, S, is called the inner Soddy centre.
