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The Incircle of a triangle
Latin: in  "inside, within" circus  "circle"
Also known as "inscribed circle", it is the largest circle that will fit inside the triangle.
Each of the triangle's three sides is a tangent to the circle.
Try this Drag the orange dots on each vertex
to reshape the triangle. Note how the incircle adjusts to always be the largest circle that will fit inside the triangle.
The center of the incircle, called the
incenter,
is the
intersection
of the
angle bisectors.
The bisectors are shown as dashed lines in the figure above.
Constructing the Incircle of a triangle
It is possible to construct the incircle of a triangle using a compass and straightedge. See
Constructing the the incircle of a triangle.
Attributes
Incenter 
The location of the center of the incircle. The point where the angle bisectors meet.

Inradius 
The radius of the incircle. The radius is given by the formula:
where:
a is the area
of the triangle. In the example above, we know all three sides, so
Heron's formula
is used.
p is the perimeter of the triangle,
the sum of its sides.

Equilateral triangle case
For the special case of an equilateral triangle
the inradius is also given by the formula
where S is the length of a side.
Related triangle topics
General
Perimeter / Area
Triangle types
Triangle centers
Congruence and Similarity
Solving triangles
Triangle quizzes and exercises
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