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A tangential quadrilateral with its incircle. In Euclidean geometry, a tangential quadrilateral (sometimes just tangent quadrilateral) or circumscribed quadrilateral is a convex quadrilateral whose sides all can be tangent to a single circle within the quadrilateral. This circle is called the incircle of the quadrilateral or its inscribed ...
The center of the incircle is a triangle center called the triangle's incenter. [1] An excircle or escribed circle[2] of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of the triangle's sides.
Kite (geometry) A kite, showing its pairs of equal-length sides and its inscribed circle. In Euclidean geometry, a kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides. Kites are also known as deltoids, [1] but the word deltoid may ...
A tangential quadrilateral is usually defined as a convex quadrilateral for which all four sides are tangent to the same inscribed circle. Pitot's theorem states that, for these quadrilaterals, the two sums of lengths of opposite sides are the same. Both sums of lengths equal the semiperimeter of the quadrilateral. [2]
In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs. Since the tangent line to a circle at a point P is ...
The leftmost and rightmost vertices have right angles. 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).
Compound of five great rhombihexahedra. Compound of five icosahedra. Compound of five octahedra. Compound of five octahemioctahedra. Compound of five small cubicuboctahedra. Compound of five small rhombicuboctahedra. Compound of five small rhombihexahedra. Compound of five small stellated dodecahedra.
Look up trapezoid in Wiktionary, the free dictionary. In geometry, a trapezoid (/ ˈtræpəzɔɪd /) in North American English, or trapezium (/ trəˈpiːziəm /) in British English, [ 1 ][ 2 ] is a quadrilateral that has one pair of parallel sides. The parallel sides are called the bases of the trapezoid. The other two sides are called the ...