Area of a Triangle inside the Incircle

BC

≈

13.32

r

≈

3.28

R

≈

6.98

area(IDE)

≈

5.13

BC×

2

r

4R

≈

5.13

Let ABC be a triangle,

r

the radius of its incircle, and

R

the radius of its circumcircle. Let D and E be the feet of the perpendiculars drawn from the center I of the incircle onto AB and AC, respectively. Then the area of the triangle IDE is

BC×

2

r

/(4R)

.