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The Sum of the Circumradii 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, 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 After work by: Antonio Gutierrez

See Problem 143. Four Triangles, Incircle, Tangent and Parallel to Side, Circumradii.

Circumcircle (Wolfram MathWorld)

Circumradius (Wolfram MathWorld)

Incircle (Wolfram MathWorld)

Parallel (Wolfram MathWorld)

Parallel Lines (Wolfram MathWorld)

"The Sum of the Circumradii of Three Subtriangles" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheSumOfTheCircumradiiOfThreeSubtriangles/

Contributed by: Jay Warendorff

After work by: Antonio Gutierrez

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