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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Answered by
9
Let radius of a circle be x
Radius of second circle : 14-x
Area of circle 1 =
Area of circle 2 =
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
Radius of second circle : 14-x
Area of circle 1 =
Area of circle 2 =
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
Aahana772:
Thanks ...bro
Answered by
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.....
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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