Concyclic points

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In geometry, a set of points is said to be concyclic if they lie on a common circle.

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.