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  | 28th Feb, 2013, 12:52: PM

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)+ (r2)= 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  | 28th Feb, 2013, 04:38: PM

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