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


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Discussion

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Copyright © 1996-2017 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 ∠CQD = ∠BSA. 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 https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.


What if applet does not run?

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

Equilic Quadrilateral

  1. Equilic Quadrilateral I
  2. Equilic Quadrilateral II
  3. Equilateral Triangles on Segments of Equilic Quadrilateral
  4. Equilic Quadrilateral I, A Variation
  5. Equilateral Triangles on Diagonals of Antiequilic Quadrilateral

|Activities| |Contact| |Front page| |Contents| |Geometry|

Copyright © 1996-2017 Alexander Bogomolny

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