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The Sum of the Square Roots of the Areas of Three Subtriangles
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 .



See Problem 142. Four Triangles, Incircle, Tangent and Parallel to Side, Areas.


"The Sum of the Square Roots of the Areas of Three Subtriangles" from The Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/TheSumOfTheSquareRootsOfTheAreasOfThreeSubtriangles/
Contributed by: Jay Warendorff
After work by: Antonio Gutierrez
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