# 10th Class Mathematics Areas Related to Circles

Areas Related to Circles

Category : 10th Class

Areas Related to Circles

• A circle is a closed curve in a plane drawn in such a way that every point on this curve is at a constant distance (r units) from a fixed point O inside it.

The fixed point O is called the centre of the circle and the constant distance r is called the length of radius of the circle.

• Circumference of a circle:

The perimeter of a circle is called its circumference. The length of the thread that winds tightly around the circle exactly once gives the circumference of the circle.

Circumference$=2\pi r=\pi d$, where r = radius and d = diameter.

Here $\pi$ (Pi) is a constant.

Note: The approximate value of n is taken as$\frac{22}{7}$or 3.14. However n is not a rational number. It is an irrational number and is defined as the ratio of circumference of a circle to its diameter.

• Area of a circle:

Area of a circle with radius r units is equal to$\pi {{r}^{2}}sq$units.

• Area of a ring:

The region enclosed between two concentric circles of different radii is called a ring.

Area of path formed$=(\pi {{R}^{2}}-\pi {{r}^{2}})sq.$ units

$=\pi ({{R}^{2}}-{{r}^{2}})sq.units$

$=\pi (R+r)(R-r)sq.units$

• Length of an arc of a circle:

Let A and B be any two points on a circle. The length of the thread that will wrap along this arc from A to B is the length of AB written as$\overset\frown{AB}$?

In a circle of radius r, we have

$\frac{l(\overset\frown{AB})}{Circumference}=\frac{{{x}^{o}}}{{{360}^{o}}}or\,l(\overset\frown{AB})=\frac{2\pi r{{x}^{o}}}{{{360}^{o}}}$

• Area of a sector:

A sector of a circle is the region enclosed by an arc of a circle and two radii to its end points. Area of sector $=\frac{{{x}^{o}}}{{{360}^{o}}}\times \pi {{r}^{2}}$where x is sector angle and r is radius of circle.

• Segment of a circle:

A segment of a circle is the region enclosed by an arc of the circle and its chord.

Area of minor setment $\text{AXB}=$area of sector OAXB - area of $\Delta \text{OAB}$

Area of major segment AYB = area of circle - area of minor segment AXB

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##### Notes - Areas Related to Circles

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