Construction of circles

A circle with center $O$ and radius $r$ is the locus of all points $P$ in the plane such that $OP = r$. Circles can be constructed using a compass and straightedge, and their properties are often used in geometric transformations, including inversion.

Important properties

• A circle is defined by its center and radius.

• Given any two points, a circle can be constructed with one as the center and the other on the circumference.

• Circles are preserved under many geometric transformations, but under inversion, lines and circles can transform into each other.