How many vertices does a circle have?

A vertex is defined as the point where two straight line segments (edges) meet to form a corner or angle. This definition governs polygons and every other straight-edged figure: a vertex requires at least two straight edges intersecting at a single point.

A circle is the locus of points equidistant from a fixed center, traced by a single continuous curved line with no straight-line segment anywhere along its boundary. Because no two straight edges ever meet on a circle, none of its points satisfy the definition of a vertex — a circle therefore has no vertices.

• No vertices — matches the definition above directly: a circle's boundary is entirely curved, so no corner point exists anywhere on it.

• Only 1 vertex — describes a figure like an angle or a cone's apex, where two straight rays or edges meet at a single corner; a circle has no straight edges to meet in the first place.

• ∞ vertices — a circle does have infinitely many points on its boundary, but ‘vertex’ specifically means a corner formed by two straight edges, not merely a point on a curve; infinite points do not create infinite corners.

• None of these — would apply only if none of the three numeric options matched a circle's vertex count, but the zero-vertex count established above is exactly one of those three options.

Therefore, a circle has no vertices, since a vertex requires two straight edges to meet and a circle's boundary is a single unbroken curve with no straight edges at all.