A circle is the set of all points in a plane that are at a fixed distance from a given point. That point is called the center.

circle

In short, a circle is round curve. The point equidistant from any point on the circle is center. It is the most important point in the circle. The distance between the center point and curve of the circle is called radius. Twice of radius is the diameter.

The radius of a circle is the distance from the center of the circle to any point on the circle. The radius is usually indicated by the letter r.

The diameter of a circle is the length of a line that goes from one side of the circle to the other and passes through the center. The diameter is twice the length of the radius, and it’s the longest possible distance across the circle. Diameter usually is indicated by the letter d.

The circumference of a circle is the distance around the circle. The formula for finding circumference is 2 times the radius times pi. Because twice the radius is the measure of the diameter, you can also figure circumference by multiplying the diameter by pi.

The area of a circle is the measure of the space inside the circle.

1. Circumference and Area of Circle  

circle-formula

These formulae gives circumference and area of the circle. Also remember that diameter is two times the radius of the circle.

2. Chord of Circle 

circle-chord

Any line segment that has both endpoints on the circle is a chord. These two points at the end of the chord are also the endpoints of an intercepted arc.

Chord that runs through the center of the circle is diameter. The diameter is the longest possible chord.

3. Arc of Circle

An arc of a circle is a portion along the circumference of the circle. A minor arc is less than 180 degrees. A semicircle is equal to 180 degrees. A major arc is greater than 180 degrees. In fact, the arc of the entire circle is 360 degrees.

A central angle of a circle is an angle that’s formed by two radii. It is called a central angle because its vertex is the center of the circle. The measurement of the central angle is the same as that of the arc formed by the endpoints of its radii. So a 90-degree central angle intercepts one-quarter of the circle, or a 90-degree arc.

circle-arc

The complete circle has angle of 360 degrees and corresponding length is called circumference of the circle. There is direct relationship between the length of the arc and the angle made by the circle.

L/(2πr) = θ/(2π)

L = θ r

4. Tangent to a Circle

A tangent line to a circle touches the circle at only one point. A good way to think of a tangent line in the real world is like a wheel rolling along a road. The road is tangent to the wheel.

  1. The radius of the circle is perpendicular to the tangent line at the point of tangency. 
  2. Two tangents to a circle from a common exterior point of the circle are equal in length.