Definition- A circle is the set of all points in a plane that are a given distance from a given point in the plane. That point is called the center, and a segment joining the center to a point on the circle is a radius.

Definition- Two coplanar circles with the same center are called cocentric circles.

Definition- Two circles are congruent whwnever a radius of one of them equals a radius of the other.

Definition- A point is inside a circle, if its distance from the center is less than the radius.

Definition- A point is outside a circle, if its distance from the center is more than the radius.

Definition- A point is on a circle if its distance from the center is equal to the length of a radius.

Definition- A chord of a circle is a segment joining any two points of the circle.

Definition- A diameter of a circle is a chord that passes through the center of the circle.

Definition- The distance from the center of a circle to a chord is the measure of the perpendicular segment from the center to the chord.

Theorem- if a radius is perpendicular to a chord, then it bisects the chord.

Theorem- If a radius of a circle bisects a chord that is not a diameter, then it is perpendicular to that chord.

Theorem- The perpendicualr bisector of a chord passes through the center of the circle.