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In Euclidean geometry, a tangential quadrilateral (sometimes just tangent quadrilateral) ... its center is the incenter and its radius is called the inradius.
The radius of this Apollonius circle is + where is the incircle radius and is the ... Tangential quadrilateral – Polygon whose four sides all touch a circle;
In Euclidean geometry, a right kite is a kite (a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other) that can be inscribed in a circle. [1] That is, it is a kite with a circumcircle (i.e., a cyclic kite). Thus the right kite is a convex quadrilateral and has two opposite right ...
Additionally, if a convex kite is not a rhombus, there is a circle outside the kite that is tangent to the extensions of the four sides; therefore, every convex kite that is not a rhombus is an ex-tangential quadrilateral. The convex kites that are not rhombi are exactly the quadrilaterals that are both tangential and ex-tangential. [16]
In Möbius geometry, tangency between a line and a circle becomes a special case of tangency between two circles. This equivalence is extended further in Lie sphere geometry. Radius and tangent line are perpendicular at a point of a circle, and hyperbolic-orthogonal at a point of the unit hyperbola.
Cyclic quadrilateral – Quadrilateral whose vertices can all fall on a single circle; Cycloid – Curve traced by a point on a rolling circle; Ex-tangential quadrilateral – Convex 4-sided polygon whose sidelines are all tangent to an outside circle; Hawaiian earring – Topological space defined by the union of circles
Newton's theorem can easily be derived from Anne's theorem considering that in tangential quadrilaterals the combined lengths of opposite sides are equal (Pitot theorem: a + c = b + d). According to Anne's theorem, showing that the combined areas of opposite triangles PAD and PBC and the combined areas of triangles PAB and PCD are equal is ...
A tangential polygon, such as a tangential quadrilateral, is any convex polygon within which a circle can be inscribed that is tangent to each side of the polygon. [21] Every regular polygon and every triangle is a tangential polygon.