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A four-sided quadrilateral not contained in a plane. The lines connecting the midpoints of opposite sides of a skew quadrilateral intersect (and bisect) each other (Steinhaus ...

If two pairs of opposite sides of a complete quadrilateral are pairs of perpendicular lines, the quadrilateral is said to be orthocentric. In such a case, the remaining sides ...

A rational quadrilateral is a quadrilateral for which the sides, polygon diagonals, and area are rational. The simplest case has sides a=52, b=25, c=39, and d=60, polygon ...

A quadrilateral in which a pair of opposite sides have the same length and are inclined at 60 degrees to each other (or equivalently, satisfy <A>+<B>=120 degrees). Some ...

The figure determined by four lines, no three of which are concurrent, and their six points of intersection (Johnson 1929, pp. 61-62). Note that this figure is different from ...

For a general quadrilateral with sides of length a, b, c, and d, the area K is given by (1) where s=1/2(a+b+c+d) (2) is the semiperimeter, A is the angle between a and d, and ...

Let a circle C_1 lie inside another circle C_2. From any point on C_2, draw a tangent to C_1 and extend it to C_2. From the point, draw another tangent, etc. For n tangents, ...

If an n-sided Poncelet transverse constructed for two given conic sections is closed for one point of origin, it is closed for any position of the point of origin. ...

An orthodiagonal quadrangle is a quadrangle whose diagonals are perpendicular to each other. If a, b, c, and d are the sides of a quadrangle, then this quadrangle is ...

The radius of a polygon's incircle or of a polyhedron's insphere, denoted r or sometimes rho (Johnson 1929). A polygon possessing an incircle is same to be inscriptable or ...