I have already discussed some part of geometry in my previous sessions. Both are related to triangles and their properties. Also, I have discussed some Important Questions of geometry. Today I will discuss circles and its properties in exam point of view. Firstly I will tell you some terms related to figure of circle.

Above figure shows that, If OC is a perpendicular to AB, C will be the mid-point of AB

i.e. AC = CB and vice-versa.

If AB is tangent, then alternate angles will be equal in given figure.

I hope you understand the above important results. Will soon update more articles on Geometry. Thanks for visiting.

Also Check: Data Interpretation

How to prepare for Quantitative aptitude section

## Basic Terminologies

**Centre:**'O' is a centre of the circle i.e. fixed point in the circle.**Radius:**OM is a radius of circle i.e.from centre to the boundary of circle.**Diameter:**Double of radius. In figure, XY is a diameter.**Circumference:**2`pi`r i.e. distance around the circle.**Secant:**A line which intersect the circle at two points. In figure, line PQ intersect circle at AB, So PQ is a secant.**Tangent:**Any line which touches the circle at only one point is tangent of circle. TU is a tangent of circle.**Chord:**Line whose end points touches the circle . RS is a chord of circle.**Segment:**Chord divides the circle into two parts. one major and other minor. Both parts are known as Segments. In figure, yellow region is a minor segment.

## Important Results of Circles

#### Area of Circle

If r is radius of circle, then area of circle = `pi r^2`

**Example1:**If area of circle is 314, then what will be the radius of circle?

**Solution:**Area = `pi r^2`

⇒ 200 = `pi r^2`

⇒ r^2 = `314/3.14` (`pi` = 3.14)

⇒ r = 10

#### Secants

In a figure given below,

**PA**is a tangent and**PRS**is a secant, then
PR `times` PS = PA^2 (Result for one tangent and one secant)

If there are two secants, for example in figure,

**PRS**and**PTU**are secants, then result followed will be:
PT `times` PU = PR `times` PS

#### Angles of same segment

Yellow part is a segment of circle.

Always remember that:

- Angles subtended by same segments are always equal. In figure, angle P and Q are equal, as they are subtended by same segment.
- Angle subtended by segment at the centre is twice the angle subtended at the boundary Angle O = 2 angle P = 2 angle Q.

Above figure shows that, If OC is a perpendicular to AB, C will be the mid-point of AB

i.e. AC = CB and vice-versa.

#### Alternate segment theorem

I hope you understand the above important results. Will soon update more articles on Geometry. Thanks for visiting.

Also Check: Data Interpretation

How to prepare for Quantitative aptitude section

Geometry(Part-3) : Circles and their properties
Reviewed by Jasleen Behl
on
Sunday, March 16, 2014
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