An orthodiagonal quadrilateral (yellow). According to the characterization of these quadrilaterals, the two red squares on two opposite sides of the quadrilateral have the same total area as the two blue squares on the other pair of opposite sides.
In Euclidean geometry, an orthodiagonal quadrilateral is a quadrilateral in which the diagonals cross at right angles. In other words, it is a four-sided figure in which the line segments between non-adjacent vertices are orthogonal (perpendicular) to each other.
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In Euclidean geometry, an orthodiagonalquadrilateral is a quadrilateral in which the diagonals cross at right angles. In other words, it is a four-sided...
Bicentric quadrilateral: it is both tangential and cyclic. Orthodiagonalquadrilateral: the diagonals cross at right angles. Equidiagonal quadrilateral: the...
an orthodiagonalquadrilateral. The result is: p.222 K = 1 2 ( a c + b d ) . {\displaystyle K={\tfrac {1}{2}}(ac+bd).} In a cyclic orthodiagonal quadrilateral...
quadrilaterals: a quadrilateral is equidiagonal if and only if its Varignon parallelogram is orthodiagonal (a rhombus), and the quadrilateral is orthodiagonal if and...
maltitudes of a quadrilateral is a perpendicular to a side through the midpoint of the opposite side. An orthodiagonalquadrilateral is a quadrilateral whose diagonals...
are perpendicular (an orthodiagonal parallelogram) a quadrilateral with four sides of equal length (by definition) a quadrilateral in which the diagonals...
exactly the tangential quadrilaterals that are also orthodiagonal. A right kite is a kite with a circumcircle. If a quadrilateral is both tangential and...
The first of these three means that the contact quadrilateral WXYZ is an orthodiagonalquadrilateral. If E, F, G, H are the midpoints of WX, XY, YZ, ZW...
opposite sides of the chord, then they are supplementary. For a cyclic quadrilateral, the exterior angle is equal to the interior opposite angle. An inscribed...
since the diagonals are perpendicular (so a right kite is an orthodiagonalquadrilateral with area K = p q 2 {\displaystyle K={\frac {pq}{2}}} ), the...
quadrilateral is an equidiagonal quadrilateral (its diagonals have equal length), and the condition that sin(θ) = 1 means that it is an orthodiagonal...
circle. This theorem is known as power of a point. A convex quadrilateral is orthodiagonal (has perpendicular diagonals) if and only if the midpoints of...
in the figure. These four points WXYZ form the vertices of an orthodiagonalquadrilateral. By applying the Pythagorean theorem to the right triangle AWP...
In geometry, Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that is, has perpendicular diagonals), then the perpendicular...
"anticenter". Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that is, has perpendicular diagonals), then the perpendicular...
"anticenter". Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that is, has perpendicular diagonals), then the perpendicular...
connecting the centers of opposite squares form a quadrilateral that is both equidiagonal and orthodiagonal (that is, whose diagonals are equal in length...
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