The Area of the Contact Triangle

r

≈

3.28

R

≈

6.98

area(ABC)

≈

58.34

area(A'B'C')

≈

13.70

rarea(ABC)

2R

≈

13.70

Let ABC be a triangle,

r

the radius of its incircle, and

R

the radius of its circumcircle. The contact triangle A'B'C' is formed by the three points of contact of the incircle with the triangle ABC. Then the area of A'B'C' is

r

×area(ABC)/(2

R

).

Details

The statement of the theorem is in Problem 82. Area of the Contact Triangle, Inradius, Circumradius.

External Links

Circumcircle (Wolfram MathWorld)

Contact Triangle (Wolfram MathWorld)

Incircle (Wolfram MathWorld)

Permanent Citation

Jay Warendorff, Antonio Gutierrez

"The Area of the Contact Triangle"
http://demonstrations.wolfram.com/TheAreaOfTheContactTriangle/
Wolfram Demonstrations Project
Published: March 7, 2011