The point where the three angle bisectors of a triangle meet.

One of a triangle's points of concurrency.

One of a triangle's points of concurrency.

Try this Drag the orange dots on each vertex
to reshape the triangle. Note the way the three angle bisectors always meet at the incenter.

One of several centers the triangle can have, the incenter is the point where the angle bisectors intersect. The incenter is also the center of the triangle's incircle - the largest circle that will fit inside the triangle.

Center of the incircle | The incenter is the center of the triangle's incircle, the largest circle that will fit inside the triangle and touch all three sides. See Incircle of a Triangle. |

Always inside the triangle | The triangle's incenter is always inside the triangle. Adjust the triangle above by dragging any vertex and see that it will never go outside the triangle |

It is possible to find the incenter of a triangle using a compass and straightedge.

See
Constructing the the incenter of a triangle.

If you know the coordinates of the triangle's vertices, you can calculate the coordinates of the incenter. See Coordinates of incenter.

Incenter |
Located at intersection of the
angle bisectors.
See |

Circumcenter |
Located at intersection of the perpendicular bisectors of the sides See |

Centroid |
Located at intersection of the medians |

Orthocenter |
Located at intersection of the altitudes |

- Triangle definition
- Hypotenuse
- Triangle interior angles
- Triangle exterior angles
- Triangle exterior angle theorem
- Pythagorean Theorem
- Proof of the Pythagorean Theorem
- Pythagorean triples
- Triangle circumcircle
- Triangle incircle
- Triangle medians
- Triangle altitudes
- Midsegment of a triangle
- Triangle inequality
- Side / angle relationship

- 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

- 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

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

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