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The Sum of the Perimeters 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. Let be the perimeter of ABC and , and be the perimeters of AA'A'', BB'B'', and CC'C'', respectively. Then . Also, opposite sides of the hexagon A'A''B'B''C'C'' are equal, that is, A'A'' = C'B'', B'B'' = A'C'', and C'C'' = A''B'.


	Contributed by: Jay Warendorff After work by: Antonio Gutierrez

The statement of the theorem is in Problem 141. Triangle, Incircle, Tangent and parallel to side, Perimeter.

Incircle (Wolfram MathWorld)

Parallel (Wolfram MathWorld)

Parallel Lines (Wolfram MathWorld)

Perimeter (Wolfram MathWorld)

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

Contributed by: Jay Warendorff

After work by: Antonio Gutierrez

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