Incenter

Consider what happens with the position of the incenter when the triangle is right, obtuse, or equilateral.

Location for right triangles:
When the triangle is right, the incenter is inside the triangle.

Location for obtuse triangles:
When the triangle is obtuse, the point that is equidistant from the sides is inside the triangle.

Location for equilateral triangles:
When the triangle is equilateral, the incenter is located at the same position as the centroid, circumcenter, and incenter.

The location of the incenter will always be inside the triangle.

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Click Here to use a GSP script for the construction of the incenter.

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