The Incircle of a triangle

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.


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 side length.

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Other triangle topics


Perimeter / Area

Triangle types

Triangle centers

Congruence and Similarity

Solving triangles

Triangle quizzes and exercises