## Pre-Requisires

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**Areas Related To Circles | Speed Notes**

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**Introduction :**

**Circumference of a circle Or Perimeter of a circle :**

The distance around the circle or the length of a circle is called its **circumference** or **perimeter**. **(Scroll down to continue …)**

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AREAS AND PERI METER RELATED TO CIRCLES

**Introduction :**

**Circumference of a circle Or Perimeter of a circle :**

The distance around the circle or the length of a circle is called its **circumference** or **perimeter**.

Circumference (perimeter) of a circle = d or 2r, where d is a diameter and r is a radius of the circle and = 227 or 3.14

**Area of a circle:**

Area of a circle = πr^{2}

**Area of a semicircle :**

Area of semicircle = 12 πr^{2}

**Area of a quadrant :**

Area of a quadrant (quarter circle) = r24

**Perimeter of a semicircle:**

Perimeter of a semicircle or protractor =πr+2r

**Area of the ring :**

Area of the ring or an annulus

= πR^{2} – πr^{2}

= π(R^{2} – r^{2})

= π(R- r)(R+r)

**Length of the arc AB**

= 2πrθ3600 or πrθ1800

**Area of a sector:**

Area of sector OACBO =πrθ3600

OR

Area of sector OACBO = 12(r×l)

**Perimeter of a sector :**

Perimeter of sector OACBO

= Length of arc AB+2r

= πrθ1800+2r

**Other important formulae :**

(i) Distance moved by a wheel in 1 revolution = Circumference of the wheel.

(ii) Number of revolutions in one minute = Distance moved in 1 minuteCircumference

(iii) Angle described by minute hand in 60 minutes =360^{0}

(iv) Angle described by hour hand in 12 hours = 360^{0}

The midpoint of the hypotenuse of a right triangle is equidistant from the vertices of the triangle.

Angle subtended at the circumference by a diameter is always a right angle.

**Area of a segment:**

(i) Area of minor segment ACBA

= Area of sector OACBO- Area of ∆OAB

= πrθ3600- 12r2sinθ

(ii) Area of major segment BDAB

= Area of the circle – Area of minor segment ACBA

=πr^{2 }– Area of minor segment ACBA

If a chord subtends a right angle at the center, then

Area of the corresponding segment = 4-12r2

If a chord subtends an angle of 60^{0} at the center, then

Area of the corresponding segment = 6-32r2

If a chord subtends an angle of 120^{0} at the center, then Area of the corresponding segment = 3-34r2

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