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