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.

Try this 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
incenter,
is the
intersection
of the
angle bisectors.
The bisectors are shown as dashed lines in the figure above.