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Equilic Quadrilateral I, A Variation: What is this about?
A Mathematical Droodle

 

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.


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Discussion

Copyright © 1996-2008 Alexander Bogomolny

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The applet may suggest the following generalization of a statement due to Jack Garfunkel concerning equilic quadrilaterals:

  Assume in a quadrilateral ABCD AD = BC, S the intersection of AD and BC. Let Q be the apex of an isosceles triangle CDQ drawn away from AB with angleCQD = angleBSA. Then S is the midpoint of the arc of the circumcircle of ΔABS containing S.

 

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.


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What if applet does not run?

The proof is identical to the one of a similar problem for equilic quadrilaterals.

Copyright © 1996-2008 Alexander Bogomolny

29713826Page copy protected against web site content infringement by Copyscape


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