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Among all quadrilaterals with a given perimeter, the one with the largest area is the square. This is called the isoperimetric theorem for quadrilaterals. It is a direct consequence of the area inequality [38]: p.114 where K is the area of a convex quadrilateral with perimeter L.
[15] [16] The right kites are exactly the kites that are cyclic quadrilaterals, meaning that there is a circle that passes through all their vertices. [17] The cyclic quadrilaterals may equivalently defined as the quadrilaterals in which two opposite angles are supplementary (they add to 180°); if one pair is supplementary the other is as well ...
Quadrilaterals that are both orthodiagonal and equidiagonal are called midsquare quadrilaterals because they are the only ones for which the Varignon parallelogram (with vertices at the midpoints of the quadrilateral's sides) is a square.
The kites are exactly the orthodiagonal quadrilaterals that contain a circle tangent to all four of their sides; that is, the kites are the tangential orthodiagonal quadrilaterals. [1] A rhombus is an orthodiagonal quadrilateral with two pairs of parallel sides (that is, an orthodiagonal quadrilateral that is also a parallelogram).
1 Properties. 2 References. 3 Further reading. Toggle the table of contents. Harmonic quadrilateral. 5 languages.
From the definition it follows that bicentric quadrilaterals have all the properties of both tangential quadrilaterals and cyclic quadrilaterals. Other names for these quadrilaterals are chord-tangent quadrilateral [ 1 ] and inscribed and circumscribed quadrilateral .
The kites are exactly the tangential quadrilaterals that are also orthodiagonal. [3] A right kite is a kite with a circumcircle . If a quadrilateral is both tangential and cyclic , it is called a bicentric quadrilateral , and if it is both tangential and a trapezoid , it is called a tangential trapezoid .
A right kite with its circumcircle and incircle. 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]