Contact Triangles of a Triangle

r

≈

1.89

T

≈

12.56

R

≈

5.83

t

≈

4.06

r

×

T

≈

23.67

R

×

t

≈

23.67

A

B

C

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.

A contact triangle is a triangle formed from the points of tangency between the sides of a triangle and its incircle or the extended sides of the triangle and one of its excircles.

Let ABC be a triangle. Let

r

and

R

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

t

and

T

be the areas of the contact triangles for the incircle and excircle. Then

rT=Rt

.