Rational Cyclic Orthodiagonal Quadrilateral
Rational Cyclic Orthodiagonal Quadrilateral
An orthodiagonal quadrilateral is a quadrilateral with perpendicular diagonals or with a perpendicular pair of opposite sides (red lines).
A cyclic quadrilateral has vertices that lie on a circle (shown in black).
A rational quadrilateral has rational sides and diagonals.
If , , are rational numbers, then two rational cyclic orthodiagonal quadrilaterals can be constructed, with either
x
y
z
ABCD
AB=2xz+
2
y
2
z
BC=-(+)
2
y
2
z
2
x
2
z
CD=(-)+
2
x
2
z
2
y
2
z
DA=2yz(+)
2
x
2
z
CA=--4xy++
2
x
2
y
2
x
2
y
2
z
4
z
BD=2(x+y)zxy-
2
z
or
AB=2(x+y)zxy-+
2
z
2
y
2
z
BC=(+)-
2
x
2
z
4
y
4
z
CD=xy-xz-yz-xy+xz+yz-+
2
z
2
z
2
y
2
z
DA=2yz(+)+
2
x
2
z
2
y
2
z
CA=-+6+8xy+-+8xy+6+
2
x
4
y
2
y
2
x
2
y
2
z
2
x
2
y
4
z
6
z
BD=2xz
2
+
2
y
2
z
These formulas generate all such quadrilaterals. The Demonstration uses the first set of formulas.
External Links
External Links
Permanent Citation
Permanent Citation
Minh Trinh Xuan
"Rational Cyclic Orthodiagonal Quadrilateral"
http://demonstrations.wolfram.com/RationalCyclicOrthodiagonalQuadrilateral/
Wolfram Demonstrations Project
Published: February 8, 2023