Inscribed and circumscribed polygons
Overview
Important
A polygon is inscribed in a circle (cyclic polygon) if all its vertices lie on the circle. A polygon is circumscribed about a circle (tangential polygon) if all its sides are tangent to the circle.
Important properties
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A triangle can always be inscribed in a circle and circumscribed about a circle.
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A quadrilateral can be inscribed in a circle if and only if its opposite angles sum to 180° (cyclic quadrilateral).
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A quadrilateral can be circumscribed about a circle if and only if the sums of lengths of its pairs of opposite sides are equal.
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Regular polygons can always be both inscribed and circumscribed.