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In geometry, a set of points is said to be 'concyclic' if they lie on a common circle.
A circle can be drawn around any triangle. A quadrilateral that can be inscribed inside a circle is said to be a cyclic quadrilateral.
In general the centre ''A'' of a circle on which points ''P'' and ''Q'' lie must be such that ''AP'' and ''AQ'' are equal distances. Therefore ''A'' must lie on the perpendicular bisector of the line segment ''PQ''. For ''n'' distinct points there are ''n''(''n''− 1)/2 such lines to draw, and the concyclic condition is that they all meet in a single point.
A quadrilateral in which the four vertices are concyclic is called a cyclic quadrilateral. More generally, a polygon in which all vertices are concyclic is called a cyclic polygon.
★ Collinear points
Concyclic points, showing that the perpendicular bisectors of pairs are concurrent
A circle can be drawn around any triangle. A quadrilateral that can be inscribed inside a circle is said to be a cyclic quadrilateral.
In general the centre ''A'' of a circle on which points ''P'' and ''Q'' lie must be such that ''AP'' and ''AQ'' are equal distances. Therefore ''A'' must lie on the perpendicular bisector of the line segment ''PQ''. For ''n'' distinct points there are ''n''(''n''− 1)/2 such lines to draw, and the concyclic condition is that they all meet in a single point.
A quadrilateral in which the four vertices are concyclic is called a cyclic quadrilateral. More generally, a polygon in which all vertices are concyclic is called a cyclic polygon.
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See also
★ Collinear points
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