to) the three sides. The center of the incircle is a triangle center called the triangle's incenter. An excircle or escribed circle of the triangle is...

circle is externally tangent to that triangle's three excircles and internally tangent to its incircle; this result is known as Feuerbach's theorem. He proved...

that the nine-point circle is tangent to the three excircles of the triangle as well as its incircle. A very short proof of this theorem based on Casey's...

excircles; they lie outside the triangle and touch one side, as well as the extensions of the other two. The centers of the incircles and excircles form...

-mixtilinear incircle. Every triangle has three unique mixtilinear incircles, one corresponding to each vertex. The A {\displaystyle A} -excircle of triangle...

Bankoff circle Circular triangle Reuleaux triangle Circumcircle Disc Incircle and excircles of a triangle Nine-point circle Circular sector Circular segment...

Great circle Great-circle distance Circle of a sphere Horocycle Incircle and excircles of a triangle Inscribed circle Johnson circles Magic circle (mathematics)...

on the tangency of the nine-point circle of a triangle with its incircle and excircles Descartes' theorem Ford circle Bankoff circle Archimedes' twin circles...

the radii of the incircle and the three excircles: a + b + c = r + r a + r b + r c . {\displaystyle a+b+c=r+r_{a}+r_{b}+r_{c}.} Acute and obtuse triangles...

Εὐκλείδης; fl. 300 BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the...