orthodiagonal

Thus these centers are the vertices of an orthodiagonal quadrilateral.

Every kite is orthodiagonal, meaning that its two diagonals are at right angles to each other.

The kites are exactly the tangential quadrilaterals that are also orthodiagonal.

A kite is an orthodiagonal quadrilateral in which one diagonal is a line of symmetry.

The orthodiagonal quadrilateral has the biggest area of all convex quadrilaterals with given diagonals.

Orthodiagonal quadrilateral: the diagonals cross at right angles.

Conversely, any convex quadrilateral where the area can be calculated with this formula must be orthodiagonal.

An orthodiagonal quadrilateral is a quadrilateral whose diagonals are perpendicular.

In a cyclic orthodiagonal quadrilateral, the anticenter coincides with the point where the diagonals intersect.

If a cyclic quadrilateral is also orthodiagonal, the distance from the circumcenter to any side equals half the length of the opposite side.

Orthodiagonal quadrilaterals are the only quadrilaterals for which the sides and the angle formed by the diagonals do not uniquely determine the area.

Another way of saying the same thing is that the center points of the four squares form the vertices of an equidiagonal orthodiagonal quadrilateral.

In Euclidean geometry, an orthodiagonal quadrilateral is a quadrilateral in which the diagonals cross at right angles.

The first of these three means that the contact quadrilateral WXYZ is an orthodiagonal quadrilateral.

A few metric characterizations of tangential quadrilaterals and orthodiagonal quadrilaterals are very similar in appearance, as can be seen in this table.

The area K of an orthodiagonal quadrilateral equals one half the product of the lengths of the diagonals p and q:

An orthodiagonal quadrilateral that is also equidiagonal is a midsquare quadrilateral because its Varignon parallelogram is a square.

A convex quadrilateral is orthodiagonal if and only if its Varignon parallelogram (whose vertices are the midpoints of its sides) is a rectangle.

Brahmagupta's theorem states that for a cyclic orthodiagonal quadrilateral, the perpendicular from any side through the point of intersection of the diagonals bisects the opposite side.

However, infinitely many other orthodiagonal and equidiagonal quadrilaterals also have diameter 1 and have the same area as the square, so in this case the solution is not unique.

A rhombus is an orthodiagonal quadrilateral with two pairs of parallel sides (that is, an orthodiagonal quadrilateral that is also a parallelogram).

As is true more generally for any orthodiagonal quadrilateral, the area A of a kite may be calculated as half the product of the lengths of the diagonals p and q:

A related characterization states that a convex quadrilateral is orthodiagonal if and only if the midpoints of the sides and the feet of the four maltitudes are eight concyclic points; the eight point circle.

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.

A formula for the area K of a cyclic orthodiagonal quadrilateral in terms of the four sides is obtained directly when combining Ptolemy's theorem and the formula for the area of an orthodiagonal quadrilateral.