MathDB

6

Part of 2016 Kyrgyzstan National Olympiad

Problems(1)

three pairwise tangent circles

Source: KGZ national 2016 6-problem

5/10/2016
Given three pairwise tangent equal circles Ωi(i=1,2,3)\Omega_i (i=1,2,3) with radius rr. The circle Γ\Gamma touches the three circles internally (circumscribed about 3 circles).The three equal circles ωi(i=1,2,3)\omega_i (i=1,2,3) with radius xx touches Ωi\Omega_i and Ωi+1\Omega_{i+1} externally (Ω4=Ω1\Omega_4= \Omega_1) and touches Γ\Gamma internally.Find xx in terms of rr
geometry proposedgeometrycircumcircle