The Area of the Contact Triangle
Let ABC be a triangle,
the radius of its incircle, and
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
×area(ABC)/(2
).
Contributed by:
Jay Warendorff
After work by:
Antonio Gutierrez
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The statement of the theorem is in
Problem 82. Area of the Contact Triangle, Inradius, Circumradius
.
Circumcircle
(
Wolfram
MathWorld
)
Contact Triangle
(
Wolfram
MathWorld
)
Incircle
(
Wolfram
MathWorld
)
"
The Area of the Contact Triangle
" from
The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheAreaOfTheContactTriangle/
Contributed by:
Jay Warendorff
After work by:
Antonio Gutierrez
Area
Plane Geometry
Triangles
The Area of a Triangle as Half a Rectangle
Largest Isosceles Triangle Inscribed in a Circle
Medial Division of Triangles
Routh's Theorem
Hadwiger-Finsler Inequality
Largest Triangle Inscribed in a Circle
Isosceles Trapezoid Area
Related Rates: Triangle Angle and Area
Contact Triangles of a Triangle
A Triangle and an External Contact Triangle
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