Maharashtra State BoardHSC Arts 11th
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Answer the following : Two circles each of radius 7 cm, intersect each other. The distance between their centres is 72 cm. Find the area common to both the circles. - Mathematics and Statistics

Sum

Answer the following :

Two circles each of radius 7 cm, intersect each other. The distance between their centres is `7sqrt(2)` cm. Find the area common to both the circles.

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Solution

Let O and O1 be the centres of two circles intersecting each other at A and B.

Then OA = OB = O1A = O1B = 7 cm

and OO12 = 98  ...(i)

Since OA2 + O1A2 = 72 + 7

= 98

= OO12  ...[From (i)]

∴ m∠OAO1 = 90°

∴ m∠OAO1B is a square.

m∠AOB = m∠AO1B = 90°

= `(90 xx pi/180)^"c"`

= `(pi/2)^"c"`

Now, A(sector OAB) = `1/2"r"^2theta`

= `1/2 xx 7^2 xx pi/2`

= `(49pi)/4"sq.cm"`

and A(sector O1AB) = `1/2"r"^2theta`

= `1/2 xx 7^2 xx pi/2`

= `(49pi)/4"sq.cm"`

A(∠OAO1B) = (side)2 = (7)2 = 49 sq.cm

∴ Required area = area of shaded portion

= A(sector OAB) + A(sector O1AB) – A(∠OAO1B)

= `(49pi)/4 + (49pi)/4 - 49`

= `(49pi)/2 - 49`

= `49(pi/2 - 1)"sq.cm"`

Concept: Area of a Sector of a Circle
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 1 Angle and its Measurement
Miscellaneous Exercise 1 | Q 2. II (02) | Page 12
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