Circles (constructions)

A circle with center $O$ and radius $r$ is the set of all points $P$ in the plane such that $OP = r$. Using compass and straightedge, you can construct circles and solve problems such as constructing a circle through three non-collinear points, or constructing tangents from a point to a circle.

Important properties

• A circle is uniquely determined by its center and radius.

• Through any three non-collinear points, there is exactly one circle (circumcircle).

• A tangent to a circle is perpendicular to the radius at the point of contact.

• Compass and straightedge constructions can be used to solve geometric problems involving circles.