Math, asked by Aahana772, 1 year ago

Two circles touches externally .The sum of their areas is 130 π sq.cm and the distance between their centres is 14 cm .Find the radii of the circles.

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Answers

Answered by iammrmitulp7n6ud
9
Let radius of a circle be x
Radius of second circle : 14-x

Area of circle 1 =
 {x}^{2} \pi
Area of circle 2 =
( {x}^{2}   + 196  - 28x)\pi
2x sq - 28x +196 = 130
2x sq - 28x +66 = 0
x sq - 14x + 33 = 0
x sq - 11x - 3x +33 = 0
x(x-11) - 3(x-11) = 0
x = 3 or x = 11

Radius is 11 and 3

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Answered by Shivika017
6
Hey Mate...!!!!!
Here's ur answer.....
CONTENT QUALITY....

Let,
the radii of two circle be r1 and r2 cm resp.. and
C1 and C2 be their centres ..Then,

= C1C2 = r1 + r2
= 14 = r1 + r2 ..........( c1c2 is given)
= r1 + r2 = 14. ..... ( 1 )
As per given condition,
= πr1^2 + πr2^2 = 130π
= r1^2 + r2^2 = 130. ..........( 2 )
Now,
(r1+ r2)^2 = r1^2 + r2^2 + 2r1r2
= 14^2 = 130 + 2r1r2. ...( usind 1 n 2)
we get,
r1r2 = 33 ...... ( 3)
Now,
( r1 – r2 )^2 = r1^2 + r2^2 - 2r1r2..

last we get
r1 – r2. = 8 ......( 4 )
Solving (1) and (2),
we get ,

r1 = 11cm. and r2 = 3cm

Hence , the radii of the circle are 11cm and 3cm.

Use attactment for diagrm.

Hope it helps u.....
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