three circles of equal radius
Source: All-Russian Olympiad 1996, Grade 9, First Day, Problem 2
April 18, 2013
geometry proposedgeometry
Problem Statement
The centers ; ; of three nonintersecting circles of equal radius are positioned at the vertices of a triangle. From each of the points ; ; one draws tangents to the other two given circles. It is
known that the intersection of these tangents form a convex hexagon. The sides of the hexagon are alternately colored red and blue. Prove that the sum of the lengths of the red sides equals the sum of the lengths of the blue sides.D. Tereshin