escribed

Escribed refers to a geometric concept where a circle is drawn tangent to one side of a triangle and the extensions of the other two sides. This circle is called an excircle, and its center is called an excenter. Each triangle has three excircles, each corresponding to one of the triangle's sides. The excircle tangent to side 'a' is often denoted as the excircle opposite vertex A.

The radius of an excircle is called an exradius. Formulas exist to calculate the exradius using the triangle's area and semi-perimeter, as well as its side lengths. For instance, if 'K' is the area of the triangle and 's' is its semi-perimeter, the exradius 'ra' corresponding to side 'a' is given by ra = K / (s - a).

The excenter of a triangle is the intersection point of the angle bisector of one interior angle and the external bisectors of the other two interior angles. These excenters are equidistant from the sides to which their corresponding excircles are tangent. The concept of escribed circles is a fundamental part of triangle geometry and has applications in various mathematical fields.