The Sum of the Perimeters of Three Subtriangles
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'.
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