Poncelet's Porism for Quadrilaterals

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Assume circle contains circle
. If it is possible to inscribe a quadrilateral touching
with its vertices and
with its sides, then it is always possible to find a quadrilateral touching both circles and passing through any point of
outside
. Such quadrilaterals are called bicentric. For this Demonstration circle
(in tan) is fixed and the position of circle
(in brown) can be changed by dragging the red center (the radius of
is obtained through Fuss's formula). You can change the position of the red vertex of the quadrilateral.
Contributed by: Jaime Rangel-Mondragon (March 2011)
Open content licensed under CC BY-NC-SA
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"Poncelet's Porism for Quadrilaterals"
http://demonstrations.wolfram.com/PonceletsPorismForQuadrilaterals/
Wolfram Demonstrations Project
Published: March 7 2011