Circle, in simple terms, is a collection of points or locus of points which are equidistant from one fixed point known as center of the circle and the distance is known as radius of the circle.

This definition shall provide us with standard equation of the circle.

Let C be the center of the circle having coordinates (a,b) and lets assume a point P(x,y) lying on the periphery or circumference of the circle, then distance between point C and point P will be equal to radius of the circle, hence we can say that (x-a)² + (y-b)² = r² (using the distance formula) which is also known as the general equation of the circle. If the center of the circle lies on the origin then equation of the circle becomes x² + y² = r².

Terms related to circle:

1. Circumference
2. Radius
3. Chord
4. Diameter
5. Arc
6. Sector
7. Segment

Circumference is nothing but perimeter of the circle. If radius of the circle is “r”, then circumference of the circle is 2πR and since 2R = D, where D is the diameter, then circumference can also be written as πD.

Radius is distance between any point on the circumference and center of the circle. In the figure given below RO and SO are the radii.

Chord of a circle is a line segment formed by connecting any two points lying on the circumference of the circle. Don’t get confused between a line and line segment. A line has an indefinite length whereas line segment has a finite length. In the below figure DE and AB are chords.

Diameter is a specific type of a chord which passes through center of the circle. Diameter is also known as the longest chord of the circle. In the below figure AB is the diameter of the circle.

Arc of a circle is portion or part of the circumference. See the figure below, the blue curved part is an example of arc of the circle. The length of the arc is in proportion with the angle made by the end points of the arc with the center of the circle.

Sector of a circle is nothing but area enclosed between arc of a circle and two radii of the circle. See the figure below.

Segment of a circle is area enclosed between chord and arc of a circle. See the figure below.

Secant of a circle is a line or a line segment which cuts the circle at two different positions. In the figure given below, blue line intersecting the circle at two points represents the secant.

Tangent of a circle is a line or line segment which touches the circumference of the circle at one point and makes an angle of 90 degrees with the radius of the circle. From any point outside the circle we can make only two tangents to a circle.

Basic Formulas related to circles

Area of a circle = πr² . In the below figure the blue part represents the area covered by the circle.

A circle circumference formula is given by C = πd = 2πr. In the below figure the black curved part is known as the circumference of the circle.

Try the questions given below, once you have gone through the above video;