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[TALLER] Online Math Open: Umbria team

Problema 9

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28/10/2019, 22:32

Convex equiangular hexagon ABCDEF has AB = CD = EF = 1 and BC = DE = F A = 4. Congruent and pairwise externally tangent circles γ1, γ2, and γ3 are drawn such that γ1 is tangent to side AB and side BC, γ2 is tangent to side CD and side DE, and γ3 is tangent to side EF and side F A. Then the area of γ1 can be expressed as (m*pi)/n for relatively prime positive integers m and n. Compute 100m + n.