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If you mean can a circle always be drawn round a quadrilateral so that the quadrilateral is enclosed within the circle then yes as long as the diameter of the circle is large enough.

If you mean can a circle always be drawn around a quadrilateral so that it passes through all vertices then only if the opposite angles of the quadrilateral add up to 180o - such quadrilaterals are called cyclic quadrilaterals.

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Q: Can a circle always be drawn around a four-sided shape?
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