Journal for Geometry and Graphics 23 (2019), No. 1, 005--027
Copyright Heldermann Verlag 2019
A Set of Rectangles Inscribed in an Orthodiagonal Quadrilateral and Defined by Pascal-Points Circles
Shaanan College, P. O. Box 906, Haifa 26109, Israel
We define the concept of a "rectangle defined by a circle that forms Pascal points and a Pascal-points circle" in an orthodiagonal quadrilateral. This rectangle is inscribed in the given orthodiagonal quadrilateral. We show that every orthodiagonal quadrilateral has an infinite set of such rectangles. We also investigate the properties of this set of rectangles: we show that the angle between the diagonals is equal in all the rectangles and we find the rectangle with the smallest area and perimeter, and more. We also examine the intersection of this set of rectangles with another set of rectangles inscribed in the orthodiagonal quadrilateral. This second set satisfies the condition that the sides of the rectangles are parallel to the diagonals of the given quadrilateral. Finally, we prove the uniqueness of the set of rectangles defined by circles that form Pascal points and Pascal-points circles.
Keywords: Rectangles inscribed in orthodiagonal quadrilateral, circle that forms Pascal points, Pascal points circle.
MSC: 51M04; 51N20
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