The Contact Triangle and Two Other Subtriangles

area(A'B'C')

≈

4.11

area(AC'A')

≈

5.01

area(CC'A')

≈

3.48

area(A'B'C')

(

area(AC'A')

+

area(CC'A')

)

≈

34.86

2

area(AC'A')

area(CC'A')

≈

34.86

Let ABC be a triangle. Let A', B', and C' be the vertices of the contact triangle (the triangle with vertices where the incircle touches the sides of ABC). If

x=area(A'B'C')

,

y=area(AC'A')

, and

z=area(CC'A')

, then

x(y+z)=2yz

.