Circles

A circle with center $O$ and radius $r$ is the set of all points $P$ in the plane such that $OP = r$. The equation of a circle with center $(a, b)$ and radius $r$ is $(x - a)^2 + (y - b)^2 = r^2.$

Important properties

• All radii of a circle are equal.

• The diameter is $2r$.

• The circumference (distance around the circle) is $2 heta r$ for angle $heta$ in radians, or $2 heta r/360^ ext{o}$ for degrees.

• The circle divides the plane into interior and exterior regions.

• Chords, tangents, and secants are important lines related to circles.