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

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Discussion

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.

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