The Sum of the Perimeters of Three Subtriangles

p

1

≈

6.54

p

2

≈

11.11

p

3

≈

18.19

p

≈

35.85

p

1

+

p

2

+

p

3

≈

35.85

A'A''	≈	2.67	B'B''	≈	3.83	C'C''	≈	4.48
C'B''	≈	2.67	A'C''	≈	3.83	A''B'	≈	4.48

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

p

be the perimeter of ABC and

p

1

,

p

2

, and

p

3

be the perimeters of AA'A'', BB'B'', and CC'C'', respectively. Then

p=

p

1

+

p

2

+

p

3

. 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'.