the excircles are always larger than the incircle and that the largest excircle is the one tangent to the longest side and the smallest excircle is tangent...

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...

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...

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...

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

to the incircle and excircles of a triangle. Terquem's other contributions to mathematics include naming the pedal curve of another curve, and counting...

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

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

Circle List of circle topics Thales' theorem Circumcircle Concyclic Incircle and excircles of a triangle Orthocentric system Monge's theorem Power center Nine-point...

orthocentric points. The common nine-point circle is tangent to all 16 incircles and excircles of the four triangles whose vertices form the orthocentric system...

Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly from the 5th century...

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...

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...

points Hyperbolic triangle (non-Euclidean geometry) Hypotenuse Incircle and excircles of a triangle Inellipse Integer triangle Isodynamic point Isogonal...

of a given circle by using only a finite number of steps with a compass and straightedge. The difficulty of the problem raised the question of whether...

for all Heronian triangles, but additionally the centers of the incircle and excircles are at lattice points.: Thm. 5  See also Integer triangle § Heronian...

solutions to the general LLL problem (the incircle and excircles of the triangle formed by the three lines). Points and lines may be viewed as special cases...

result is that the incircles can be exchanged for the excircles to the same triangles (tangent to the sides of the quadrilateral and the extensions of...

the plane of the reference triangle and associated with it in some way. For example, the circumcircle and the incircle of the reference triangle are triangle...

titled Volume I, From Thales to Euclid and Volume II, From Aristarchus to Diophantus. It got positive reviews and is still used today. Ten years later,...

triangle, and its center is the center of mass of the perimeter of the triangle.) Any vertex, the tangency of the opposite side with the incircle, and the Gergonne...

where its incircle is tangent to the side. The two circles tangent to these three circles are separated by the incircle, one interior to it and one exterior...

semiperimeter also applies to tangential quadrilaterals, which have an incircle and in which (according to Pitot's theorem) pairs of opposite sides have...

In geometry, the incircle of the medial triangle of a triangle is the Spieker circle, named after 19th-century German geometer Theodor Spieker. Its center...

contact of the incircle with the sides of ABC Tangential triangle The triangle whose vertices are the points of contacts of the excircles with the respective...

circle of infinite radius. In every triangle a unique circle, called the incircle, can be inscribed such that it is tangent to each of the three sides of...

which connects a point of tangency of the circle to which the triangle's excircles are internally tangent, to the opposite vertex of the triangle. The two...

of the incircle of that face. If the exsphere radius is denoted rex, the radius of this incircle rin and the dihedral angle between the face and the extension...

Leon (Greek: Λέων) was an Ancient Greek mathematician and pupil of Neocleides, who was active from around 370 to 340 BCE. His book Elements was overshadowed...