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

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: Calculator 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

Calculator

Related triangle topics

General

• Triangle definition
• Hypotenuse
• Triangle interior angles
• Triangle exterior angles
• Pythagorean Theorem
• A graphical proof of the Pythagorean Theorem
• Pythagorean triples
• Triangle circumcircle
• Triangle incircle
• Triangle medians
• Midsegment of a triangle
• Triangle inequality
• Side / angle relationship

Perimeter / Area

• Perimeter of a triangle
• Area of a triangle
• Heron's formula
• Area of an equilateral triangle
• Area by the "side angle side" method
• Area of a triangle with fixed perimeter

Triangle types

• Right triangle
• Isosceles triangle
• Scalene triangle
• Equilateral triangle
• Equiangular triangle
• Obtuse triangle
• Acute triangle
• 3-4-5 triangle
• 30-60-90 triangle
• 45-45-90 triangle

Triangle centers

• Incenter of a triangle
• Circumcenter of a triangle
• Centroid of a triangle
• Orthocenter of a triangle
• Euler line

Congruence and Similarity

• Congruent triangles

Solving triangles

• Solving the Triangle
• Law of sines
• Law of cosines

Triangle quizzes and exercises

• Triangle type quiz
• Ball Box problem
• How Many Triangles?
• Satellite Orbits