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.
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
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.
||The location of the center of the incircle. The point where the angle bisectors meet.
||The radius of the incircle. The radius is given by the formula:
a is the area
of the triangle. In the example above, we know all three sides, so
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
Perimeter / Area
Congruence and Similarity
Triangle quizzes and exercises
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