Definition:Concyclic Points

Definition

A set of $4$ or more points $S = \set {P_1, P_2, \ldots, P_n}$ is concyclic if they all lie on the circumference of a circle.

In the above diagram, points $A, B, C, D$ are concyclic, as they all lie on the circumference of the circle centered at $O$.

Also see

• Vertices of Regular Polygon are Concyclic

• Three Points Describe a Circle, demonstrating that any $3$ non-collinear points always lie on the circumference of a circle, which is why the definition specifies a set of $4$ or more points

• Results about concyclic points can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): concyclic
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): concyclic
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): concyclic

• Weisstein, Eric W. "Concyclic." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Concyclic.html