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


This entry contributed by Floor van Lamoen

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Yiu, P. "Notes on Euclidean Geometry." 1998.

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Orthodiagonal Quadrangle

Cite this as:

van Lamoen, Floor. "Orthodiagonal Quadrangle." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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