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Circle theorems and Properties |

## Circle:

At this stage, we study plane figures which are in 2 dimensions. Circle is one of them. Circle is said to be an important part of geometry because it has a wide range of applications. When we see around many objects have circular portion. Take an example of a water bottle, from its cover to bottom it is circular. To make it, there must be requirement of knowledge of circle and circle formulas.

**Definition of ****circle****:**

We can define circle as closed figure round in shape. Or,

Circle is a collection of points which is equidistant from a given fixed point. Or,

Circle is a curve which follows a path which is all round equidistant from a fixed point.

## Terms used in circle:

**Radius:** The line segment joining the centre to any point on the circle.

**Diameter: **The line segment joining two points on the circle and passes through centre is called diameter. Or, say the longest chord of circle.

**Chord: **The line segment joining any two point on the circle is called chord.

**Arc: **A part of circumference of circle whose end points joined by chord. Smaller part is minor arc and larger part is major arc.

**Sector: **The space covered by arc and two radius in a circle is Sector.

**Tangent: **A straight line which only touches the circle and is in the plane of circle.

** Circumference: **The length of curved path of circle is called circumference.

**Circle Formulas:**

**r** is symbol for radius of circle.

**d** is symbol for diameter of circle.

**c** is symbol for circumference of circle.

**Circle formulas are:**

**Diameter of circle = 2r****Circumference of circle = 2πr**(where π = \(\frac{22}{7}\))**Area of circle = πr**^{2}

**Extended circle formulas:**

**Length of arc =**\(\frac{ϴ}{360⁰}\)**x 2πr**(where ϴ = angle subtended by arc at centre)**Area of sector =**\(\frac{ϴ}{360⁰}\)**x πr**(where ϴ = angle subtended by sector at centre)^{2}

**Examples of circles:**

*If the diameter of a circle is 14 cm, Find the area of circle.*

**Solution:**

D = 2r

r = D/2

r = 7 cm

Area = **πr ^{2}
**Area= \(\frac{22}{7}\)x 7

^{2 =}154 cm

^{2}

*If circumference of circle is 308cm. Find the area of circle.*

**Solution:**

Circumference = 2πr = 308 cm

r = \(\frac{308}{2π}\) = 49

Area = **πr ^{2
=}**\(\frac{22}{7}\) x (49)

^{2}= 7546 cm

^{2}

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