DOSEN PROFIL LENGKAP

of the incircle is a triangle center called the triangle's incenter. An excircle or escribed circle of the triangle is a circle lying outside the triangle...

also been called an exscriptible quadrilateral. The circle is called its excircle, its radius the exradius and its center the excenter (E in the figure)...

{a+b+c}{2}}.} In any triangle, any vertex and the point where the opposite excircle touches the triangle partition the triangle's perimeter into two equal...

circles Schoch circles Woo circles Apollonius circle of the excircles Brocard circle Excircle Incircle Lemoine circle Lester circle Malfatti circles Mandart...

TC be the extouch points in which the A-excircle meets line BC, the B-excircle meets line CA, and the C-excircle meets line AB, respectively. The lines...

states more generally 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...

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...

corresponding extended base sides but not the base sides themselves. The excircles of a triangle, as well as the triangle's inconics that are not inellipses...

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...

{\displaystyle r^{2}+r_{a}^{2}+r_{b}^{2}+r_{c}^{2}<8R^{2},} in terms of the excircle radii ra , rb , and rc , again with the reverse inequality holding for...

triangle's nine-point circle is externally tangent to that triangle's three excircles and internally tangent to its incircle; this result is known as Feuerbach's...

incircles, one corresponding to each vertex. The A {\displaystyle A} -excircle of triangle A B C {\displaystyle ABC} is unique. Let Φ {\displaystyle \Phi...

collinearities. Any vertex, the tangency of the opposite side with an excircle, and the Nagel point are collinear in a line called a splitter of the triangle...

distance between the circumscribed circle's center and the center of the excircle of an ex-tangential quadrilateral. Critical points of a cubic function...

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

three excircles are positive integers. Specifically, for a primitive triple the radius of the incircle is r = n(m − n), and the radii of the excircles opposite...

points of tangency formed by the opposing excircle and a larger circle that is tangent to all three excircles. In the literature, the term "Apollonius...

the Bevan circle, that is the circle through the centers of the three excircles of a triangle. The Bevan point of a triangle is the reflection of the...

formula, for example using trigonometry as below, or the incenter and one excircle of the triangle, or as a special case of De Gua's theorem (for the particular...

right triangle equals the sum of 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}...

r b , r c {\displaystyle r_{a},\,r_{b},\,r_{c}} are the radii of the excircles tangent to sides a, b, c respectively. We also have T = 1 2 D 2 ( sin...

triple of circles having tangencies at the points where one of the three excircles is tangent to these lines. The pairs of tangent circles to these three...

Ex-tangential quadrilateral: the four extensions of the sides are tangent to an excircle. An equilic quadrilateral has two opposite equal sides that when extended...

circles. The Spieker center of a triangle is the radical center of its excircles. Several types of radical circles have been defined as well, such as the...

Construction of the center of a Thales' circle, Construction of the center of the Excircle of a triangle, Voronoi diagram boundaries consist of segments of such lines...

"external" version of this theorem, where the incircle is replaced by an excircle and the two additional circles are external to the circumcircle, is found...

distant from the lines, the excenters, which form the centers of the excircles of the given triangle. The incenter and excenters together form an orthocentric...

involves the excircles present at each node. The three children of any parent triangle “inherit” their inradii from the parent: the parent's excircle radii become...

1 + r 3 = r 2 + r 4 . {\displaystyle r_{1}+r_{3}=r_{2}+r_{4}.} If the excircles to the same four triangles opposite the vertex ⁠ P {\displaystyle P} ⁠...

times the altitude from that base. If the line is instead tangent to the excircle opposite, say, vertex A of the triangle, then − a a ′ + b b ′ + c c ′ =...

Intersection of the lines connecting each vertex to the point where an excircle touches the opposite side. X9 Mittenpunkt M ( b + c − a ) : ( c + a − b...

the radius of the triangle's incircle, ra, rb, rc as the radii of its excircles, and R again as the radius of its circumcircle, the following relations...

within the triangle, tangent to its sides at the contact points of its excircles (which are also the vertices of the extouch triangle and the endpoints...

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

concerns the exradii ra, rb, rc, and rd in the same four triangles (the four excircles are each tangent to one side of the quadrilateral and the extensions of...

circumscribing △ A ∗ B ∗ C {\displaystyle \triangle A^{*}B^{*}C} becomes an excircle l ′ {\displaystyle l'} of △ A ′ B ′ C ′ {\displaystyle \triangle A'B'C'}...

(non-Pythagorean) triangles with integer radii for the incircle and each excircle. A family of decomposable ones is given by a = 4 n 2 {\displaystyle a=4n^{2}}...

b . {\displaystyle b+c:c+a:a+b.} S is the radical center of the three excircles. S is the cleavance center of triangle △ABC S is collinear with the incenter...

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

of his work on the method of moving axes. Hayward called a hyperbola an excircle in his Algebra of Coplanar Vectors and Trigonomety. Chapter 6 considered...

Incircle and excircles...

{\displaystyle r_{\text{A}},r_{\text{B}},r_{\text{C}}} be the radii of the three excircles. Then 1 r = 1 r A + 1 r B + 1 r C {\displaystyle {\frac {1}{r}}={\frac...

point X(9) Mittenpunkt symmedian point of the triangle formed by the centers of the three excircles X(10) Spieker center center of the Spieker circle...

the adjacent faces internally. It is the 3-dimensional equivalent of the excircle. The sphere is more generally well-defined for any face which is a regular...

tangency of the nine-point circle of a triangle with its incircle and excircles Descartes' theorem on the radii of four pairwise tangent circles Ford...

{\sqrt {z}}\cos {\frac {C}{2}}=0,} while the equation for, for example, the excircle adjacent to the side segment opposite vertex A can be written as ± − x...

triangle vertex lies at the point on the triangle's side where one of the excircles of the triangle is tangent to that side. This point is also called a splitting...

there are four solutions to the general LLL problem (the incircle and excircles of the triangle formed by the three lines). Points and lines may be viewed...

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...

triangle and △TATBTC the triangle formed by the outer tangents to its three excircles. These two triangles are similar and the Clawson point is their center...

and its perimeter P, as well as the radii ri of its incircle and three excircles as follows: a = 2 q p b = q ′ p ′ c = p p ′ − q q ′ = q p ′ + q ′ p radii...

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

three sides), the exradii ra, rb, and rc (each being the radius of an excircle tangent to side a, b, or c respectively and tangent to the extensions of...

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

△I1I2I3 of △ABC. The triangle whose sidelines are externally tangent to the excircles of △ABC is the extangents triangle of △ABC. △ABC and its extangents triangle...

is an isoperimetric point of △ABC in the sense of Veldkamp, then the excircles of triangles △PBC, △PCA, △PAB are pairwise tangent to one another and...

triangle formed by the lines which are externally tangent to the three excircles of the Yff central triangle of △ABC. Let I be the incenter of △ABC. Let...

unique ellipse tangent to a triangle's sides at the contact points of its excircles Kiepert parabola Yff parabola Weisstein, Eric W. "Circumconic." From MathWorld--A...

circle, centered at the Spieker center, which is orthogonal to the three excircles of the medial triangle. de Villiers, Michael (June 2006). "A generalisation...

connecting the tangencies of the Malfatti circles with the centers of the excircles of the triangle. Other triangle centers also associated with the Malfatti...

of the triangle. It touches the sides at the points of contact of the excircles (see diagram). For   s = | O B | 2 | O B | 2 + | A B | 2 , t = | O A |...

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

Feuerbach's theorem that the nine-point circle is tangent to the incircle and excircles of a triangle. Terquem's other contributions to mathematics include naming...