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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 February 2013, 12:52 PM
Answered by 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 Expert 28th February 2013, 4:38 PM
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