What is "in circle o?

In geometry, a circle inscribed within a triangle or another polygon is referred to as an "inscribed circle" or "incircle". The center of the incircle is called the incenter, and is equidistant from the sides of the polygon. The radius of the incircle is known as the inradius.

The incircle touches the sides of the polygon at a point called the point of tangency. The segments connecting the incenter to the points of tangency are known as the angle bisectors of the angles of the polygon.

The incenter is also the intersection point of the angle bisectors of the angles of a triangle. This property can be used to construct the incircle of a triangle using compass and straightedge.

The area of the incircle can be calculated using the formula: A = πr², where r is the radius of the incircle.

Incenters and incircles are commonly used in various geometric problems and proofs, particularly in the context of triangles and other polygons.