Inscribing a quadrilateral in a circle

Below you have a quadrilateral with the perpendicular bisectors of the sides already drawn in. Your goal is to insribe the quadrilateral in a circle.

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What do you notice about the perpendicular bisectors when the quadrilateral is inscribed in the circle?
Can the perpendiular bisectors be the same line?
Does the quadrilateral have to be convex?
Does the same rule apply for concave quadrilaterals?

Jackie Southard, June 26, 2008, Created with GeoGebra