Geodesic
A Set of Rectangles Inscribed in an Orthodiagonal Quadrilateral and Defined by Pascal-Points Circles
Journal for geometry and graphics, Tome 23 (2019) no. 1, pp. 5-27

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 51M04, 51N20
Mots-clés : Rectangles inscribed in orthodiagonal quadrilateral, circle that forms Pascal points, Pascal points circle 
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     author = {D. Fraivert },
     title = {A {Set} of {Rectangles} {Inscribed} in an {Orthodiagonal} {Quadrilateral} and {Defined} by {Pascal-Points} {Circles}},
     journal = {Journal for geometry and graphics},
     pages = {5--27},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2019},
     url = {http://geodesic.mathdoc.fr/item/JGG_2019_23_1_JGG_2019_23_1_a1/}
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D. Fraivert . A Set of Rectangles Inscribed in an Orthodiagonal Quadrilateral and Defined by Pascal-Points Circles. Journal for geometry and graphics, Tome 23 (2019) no. 1, pp. 5-27. http://geodesic.mathdoc.fr/item/JGG_2019_23_1_JGG_2019_23_1_a1/