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What are the sidelengths of the triangle ?

Source: ISI Entrance 2015

May 10, 2015
geometrycirclesTriangles

Problem Statement

Let γ1,γ2,γ3\gamma_1, \gamma_2,\gamma_3 be three circles of unit radius which touch each other externally. The common tangent to each pair of circles are drawn (and extended so that they intersect) and let the triangle formed by the common tangents be △XYZ\triangle XYZ . Find the length of each side of △XYZ\triangle XYZ
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