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CBSE Class 10 Answered

Two circles touch internally.The sum of their areas is 116 ?(pi) and the distance between their centers is 6cm. Find the radii of the circles.
Asked by | 28 Feb, 2013, 12:52: PM
answered-by-expert Expert Answer
Let the radius of 2 circles be r1 and r2
Sum of area = 116 pi
pi(r1)2 + pi(r2)2 = 116*pi
i.e. (r1)2 + (r2)2 = 116
 
Also, r1 - r2 = 6 
r1 = 6+r2
Substituting it back in the above equation
 
(6+r2)2 + (r2)2 = 116
2(r2)2 + 12r2 + 36 = 116
2(r2)2 + 12r2 -80 = 0
(r2)2 + 6r2 - 40 = 0
(r2+10) (r2 - 4) = 0
r2 = -10 or r2 = 4
Since, radius of a circle can't be negative, hence, r2 = 4cm and r1 = 10 cm
Answered by | 28 Feb, 2013, 04:38: PM

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