The Area of a Triangle inside the Incircle

AB

≈

10.09

AC

≈

9.01

r

≈

2.82

area(IDE)

≈

3.65

area(ABC)

≈

41.80

AB

×

AC

×

area(IDE)

≈

332.10

2

r

×

area(ABC)

≈

332.10

Let ABC be a triangle and let

r

be the radius of its incircle with center I. Let D and E be the feet of the perpendiculars from I onto AB and AC, respectively. Then

AB×AC×area(IDE)=

2

r

×area(ABC)

.