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...

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...

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...

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...

triangle of a triangle is formed by joining the points at which the three excircles touch the triangle. The vertices of the extouch triangle are given in...

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...

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

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...

function of its side lengths and the perpendicular distances of its vertices from an arbitrary line tangent to its incircle. The theorem is named after...

{\displaystyle a,b,c} constitute the sides of a triangle and the triangle's centroid is inside the incircle then the equation a x 2 + b x + c = 0 {\displaystyle...

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...

(the middle and right column in the table), as can be seen in the table below. Thus a convex quadrilateral has an incircle or an excircle outside the...

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...

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

triangle's orthocenter, Nagel point, and various other notable points, and has center on the nine-point circle. Inconics Incircle, the unique circle that is internally...

incircle. Further important inellipses are the Steiner inellipse, which touches the triangle at the midpoints of its sides, the Mandart inellipse and...

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

those that have an incircle that is tangent to each side of the polygon. In this case the incenter is the center of this circle and is equally distant...

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

independently proposed and solved this problem in 1905. An "external" version of this theorem, where the incircle is replaced by an excircle and the two additional...

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...

targets Horocycle – Curve whose normals converge asymptotically Incircle and excircles of a triangle – Circles tangent to all three sides of a trianglePages...

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

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...

adjacent touch point of an incircle or excircle are congruent, A ′ T B ≅ A ′ T C {\displaystyle A'T_{B}\cong A'T_{C}} (blue segments) and B ′ T A ≅ B ′ T C {\displaystyle...

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...

triangle ABC and orthologic with it. Medial triangle Anticomplementary triangle The triangle whose vertices are the points of contact of the incircle with 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...