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The Sum of the Circumradii of Three Subtriangles

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Let ABC be a triangle. Let A'A'', B'B'', and C'C'' be tangents to the incircle of ABC and parallel to BC, AC, and AB, respectively, so that A'', B' are on AB, B'', C' are on BC, and C'', A' are on CA . Let be the circumradius of ABC and , , and be the circumradii of AA'A'', BB'B'', and CC'C'', respectively. Then .

Contributed by: Jay Warendorff (March 2011)
After work by: Antonio Gutierrez
Open content licensed under CC BY-NC-SA

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