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The Sum of the Square Roots of the Areas 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 such that A'', B' are on AB, B'', C' are on BC, and C'', A' are on CA. Let be the area of ABC and , , and be the areas 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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