Inscribed Circle
An inscribed circle, also known as an incircle, is a circle that is drawn inside a polygon, touching all its sides. The center of this circle is called the incenter, which is the point where the angle bisectors of the polygon intersect. The radius of the inscribed circle is known as the inradius.
In a triangle, the inscribed circle is particularly significant as it represents the largest circle that can fit within the triangle. The area of the triangle can be calculated using the inradius and the semiperimeter, which is half the sum of the triangle's sides. This concept is essential in geometry and is often used in various mathematical applications.