4th CaMO 1972 Problem 1 Three unit circles are arranged so that each touches the other two. Find the radii of the two circles which touch all three.
The two circles have center at the center of the triangle, which is the centroid and hence a distance 2/3 √3 from the center of each of the unit circles. The two required radii are therefore 2/√3 ± 1. 4th CaMO 1972 © John Scholes jscholes@kalva.demon.co.uk 10 June 2002