In Euclidean geometry, a tangential polygon, also known as a circumscribed polygon, is a convex polygon that contains an inscribed circle (also called...

approximation of convex polygons Tangential polygon – Convex polygon that contains an inscribed circle Definition and properties of convex polygons with interactive...

A tangential polygon is a polygon each of whose sides is tangent to a particular circle, called its incircle. Every triangle is a tangential polygon, as...

called the circumcentre, can be considered a centre of the polygon. If a polygon is both tangential and cyclic, it is called bicentric. (All triangles are...

are no longer sufficient to determine the shape of the pentagon. A tangential polygon (one that has an incircle tangent to all its sides) is equilateral...

each side of the polygon. Every regular polygon and every triangle is a tangential polygon. A cyclic polygon is any convex polygon about which a circle...

symmetry orbit. The polygon is also equilateral and tangential. The property of regularity may be defined in other ways: a polygon is regular if and only...

to every side at the midpoint. Thus a regular polygon is a tangential polygon. A regular n-sided polygon can be constructed with compass and straightedge...

Equilateral polygon Penrose tile Polyform Regular polygon Simple polygon Tangential polygon Triangle – 3 sides Acute triangle Equilateral triangle Heptagonal...

quadrilaterals, and circumscriptible quadrilaterals. Tangential quadrilaterals are a special case of tangential polygons. Other less frequently used names for this...

case the polygon is said to be a tangential polygon. A polygon inscribed in a circle is said to be a cyclic polygon, and the circle is said to be its...

square is equable. A tangential polygon is a polygon in which the sides are all tangent to a common circle. Every tangential polygon may be triangulated...

the dual (a tangential polygon), and shorter sides to smaller angles.[citation needed] Further, congruent sides in the original polygon yields congruent...

sums of the previous n-gon. A tangential polygon is one having an inscribed circle tangent to each side of the polygon; these tangency points are thus...

group of triangle centers. For polygons with more than three sides, the incenter only exists for tangential polygons: those that have an incircle that...

cyclic polygons: the circumcentre is equidistant from each of the vertices. Likewise, the incentre of a triangle or any other tangential polygon is equidistant...

In geometry, a bicentric polygon is a tangential polygon (a polygon all of whose sides are tangent to an inner incircle) which is also cyclic — that is...

and s is the semiperimeter (in fact, this formula holds for all tangential polygons), and: Lemma 2  T = r a ( s − a ) = r b ( s − b ) = r c ( s − c )...

generally, a polygon with any number of sides that has an inscribed circle (that is, one that is tangent to each side) is called a tangential polygon. Circumcenter –...

reference triangle is the Gergonne triangle of the tangential triangle. Tangential quadrilateral Tangential polygon Altshiller-Court, Nathan. College Geometry...

In fact, every regular polygon is a circumgonal region, as is more generally every tangential polygon. But not every polygon is a circumgonal region:...

perpendicular line through the centroid of an arbitrary polygon or the incenter of a tangential polygon, depending on the source. Likewise, a right bipyramid...

bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle). The common length of the sides equals the radius...

Set of circles related by tangency Tangential polygon – Convex polygon that contains an inscribed circle Tangential quadrilateral Roulettes Centered trochoid –...

or spherical coordinate system the inradius of a triangle or other tangential polygon the ratio of a geometric series (e.g. arn−1) the remainder resulting...

quadrilateral (its diagonals are at right angles) and, when convex, a tangential quadrilateral (its sides are tangent to an inscribed circle). The convex...

to 2 T {\displaystyle 2T} . Equality holds only if the polygon is a parallelogram. The tangential triangle of a reference triangle (other than a right triangle)...

every face must have an inscribed circle (that is, it must be a tangential polygon), and all of these inscribed circles must belong to a single sphere...

undermines the geometry, and so on. The longer explanation is that any tangential perturbation brings a body closer to one neighbor and further from another;...

differentiable paths with nowhere vanishing derivatives), and is the degree of the tangential Gauss map. This is called the turning number, rotation number, rotation...