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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
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
.
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