# Circle

## Definition

A closed, round geometric figure in which the set of all the points in the plane is equidistant from a given point called ‘center’.

## Parts and Properties

1) Radius – The line that joins the center of the circle to the outer boundary. It is usually represented by ‘r’ or ‘R’. The plural of radius is called radii.

2) Diameter – The line segment whose endpoints lie on the circle and that passes through the center. Its length is twice the length of a radius. It is represented by as -‘d’ or ‘D’.

So, r = d/2 or R = D/2

3) Chord – The line segment whose endpoints lie on the circle, thus dividing a circle into two regions. The diameter is the longest chord of a circle.

4) Secant – An extended chord that cuts the circle at two distinct points.

5) Arc – The connected section of the circumference of a circle.

6) Tangent – A line that touches the circumference of a circle at a point.

7) Sector – A region bounded by two radii of equal length with a common center.

8) Segment – The segment of a circle is the region bounded by a chord and the arc subtended by the chord.

## Formulas

### Circumference

Also known as the perimeter, it is the total distance covered around the circle. The formula is given below:

Circumference (C) = 2πr, here r = radius, and π = 3.141 = 22/7

Problem: Finding the circumference of a circle when only the DIAMETER is known

The diameter of a circle is 6 centimeters. Find the circumference

Solution:

As we know,
C = 2πr, here r = d/2 = 6/2 cm = 3 cm
Hence, C = 2 x 3.14 × 3
= 18.84 cm

Problem: Finding the circumference of a circle when only the RADIUS is known

The radius of a circle is 4 inches. Find the circumference

Solution:

As we know,
C = 2πr , here r = 4 inches
= 2 × 3.14 × 4
= 25.12 inches

### Area

It is the total space enclosed inside the boundary of the circle. It is also known as the ‘surface area of the circle’. The formula is given below:

Area (A) = πr2, here r = radius, and π = 3.141 = 22/7

Problem: Finding the area of a circle when only the RADIUS is known

Find the area of a circle with a radius of 9 cm

Solution:

As we know,
A = πr2, here r = 9 cm
= 3.14 × 9 × 9
= 254.34 cm2

Problem: Finding the area of a circle when only the DIAMETER is known

Find the area of a circle with a diameter of 10 cm

Solution:

As we know,
A = πr2 and r = d/2 = 10/2 = 5 cm
= 3.14 × 5 × 5
= 78.5 cm2

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