The Incenter of a triangle
Latin: in  "inside, within" centrum  "center"
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.
Properties of the incenter
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 
Finding the incenter of a triangle
It is possible to find the incenter of a triangle using a compass and straightedge.
See
Constructing the the incenter of a triangle.
Coordinate geometry
If you know the coordinates of the triangle's vertices, you can calculate the coordinates of the incenter.
See Coordinates of incenter.
Summary of triangle centers
There are many types of triangle centers. Below are four of the most common.
In the case of an equilateral triangle,
all four of the above centers occur at the same point.
Other triangle topics
General
Perimeter / Area
Triangle types
Triangle centers
Congruence and Similarity
Solving triangles
Triangle quizzes and exercises
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