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Orthodiagonal Quadrangle


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 orthodiagonal iff a^2+c^2=b^2+d^2.

If ABCD is a cyclic orthodiagonal quadrangle, then the quadrangle formed by the tangents to the circumcircle through the vertices of ABCD form a bicentric quadrilateral A^'B^'C^'D^'. The circumcenters of ABCD and A^'B^'C^'D^' and the point of intersection of the diagonals of ABCD are collinear.


See also

Quadrangle

This entry contributed by Floor van Lamoen

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References

Yiu, P. "Notes on Euclidean Geometry." 1998. http://www.math.fau.edu/yiu/EuclideanGeometryNotes.pdf.

Referenced on Wolfram|Alpha

Orthodiagonal Quadrangle

Cite this as:

van Lamoen, Floor. "Orthodiagonal Quadrangle." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/OrthodiagonalQuadrangle.html

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