A Triangle and an External Contact Triangle

r

≈

3.70

T

≈

11.27

R

≈

5.60

t

≈

14.87

2

r

×

T

≈

83.33

R

×

t

≈

83.33

Extend two sides of a triangle and construct the circle tangent to those sides and the third side of the triangle. The resulting circle is called an excircle. The triangle formed by the three points of tangency is called an external contact triangle.

Let ABC be a triangle. Let

r

and

R

be the radii of the circumcircle and an excircle of ABC. Let

t

be the area of ABC and

T

be the area of the external contact triangle. Then

2rT=Rt

.

Details

The statement of the theorem is in Problem 83. Area of an Excircle Contact Triangle, Exradius, Circumradius.

External Links

Circumcircle (Wolfram MathWorld)

Excircles (Wolfram MathWorld)

Permanent Citation

Jay Warendorff, Antonio Gutierrez

"A Triangle and an External Contact Triangle"
http://demonstrations.wolfram.com/ATriangleAndAnExternalContactTriangle/
Wolfram Demonstrations Project
Published: March 7, 2011