MathDB

11.6

Part of VII Soros Olympiad 2000 - 01

Problems(1)

sum of radii of 6 inner circles = diameter of large circle, tangent to all 6

Source: VII Soros Olympiad 2000-01 Round 1, 11.6

7/4/2021
A circle is tangent internally by 66 circles so that each one is tangent internally to two adjacent ones and the radii of opposite circles are pairwise equal. Prove that the sum of the radii of the inner circles is equal to the diameter of the given circle.
tangent circlesgeometry