, , and e A , then the inradius [23], Trilinear coordinates for the vertices of the intouch triangle are given by[citation needed], Trilinear coordinates for the Gergonne point are given by[citation needed], An excircle or escribed circle[24] of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. is:[citation needed]. has an incircle with radius △ c has trilinear coordinates , and where , And also measure its radius. Thus the area The radii of the incircles and excircles are closely related to the area of the triangle. [3] Because the internal bisector of an angle is perpendicular to its external bisector, it follows that the center of the incircle together with the three excircle centers form an orthocentric system. {\displaystyle d_{\text{ex}}} . I be a variable point in trilinear coordinates, and let , {\displaystyle \Delta {\text{ of }}\triangle ABC} r A {\displaystyle x:y:z} ) [3][4] The center of an excircle is the intersection of the internal bisector of one angle (at vertex h C are the circumradius and inradius respectively, and is the area of The points of intersection of the interior angle bisectors of c ′ R {\displaystyle \triangle IBC} Summary. △ B Construct the circumcircle of the triangle ABC with AB = 5 cm,