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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 ...

The figure formed when the midpoints of the sides of a convex quadrilateral are joined in order is a parallelogram. Equivalently, the bimedians bisect each other. The area of ...

A maltitude ("midpoint altitude") is a perpendicular drawn to a side of a quadrilateral from the midpoint M_i of the opposite side. If the quadrilateral is cyclic, then the ...

If the four points making up a quadrilateral are joined pairwise by six distinct lines, a figure known as a complete quadrangle results. A complete quadrangle is therefore a ...

For a cyclic quadrilateral, the sum of the products of the two pairs of opposite sides equals the product of the diagonals AB×CD+BC×DA=AC×BD (1) (Kimberling 1998, p. 223). ...

The point of concurrence of the four maltitudes of a cyclic quadrilateral. Let M_(AC) and M_(BD) be the midpoints of the diagonals of a cyclic quadrilateral ABCD, and let P ...

In a cyclic quadrilateral ABCD having perpendicular diagonals AC_|_BD, the perpendiculars to the sides through point T of intersection of the diagonals (the anticenter) ...

The circles on the polygon diagonals of a complete quadrilateral as diameters are coaxal. Furthermore, the orthocenters of the four triangles of a complete quadrilateral are ...

Pick a point O in the interior of a quadrilateral which is not a parallelogram. Join this point to each of the four vertices, then the locus of points O for which the sum of ...

A plane figure consisting of four points, each of which is joined to two other points by a line segment (where the line segments may intersect). A quadrangle may therefore be ...