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 the 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:

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:

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 = πr^{2}, here r = 9 cm = 3.14 × 9 × 9 = 254.34 cm^{2}

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 = πr^{2} and r = d/2 = 10/2 = 5 cm = 3.14 × 5 × 5 = 78.5 cm^{2}