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Q.

Two circles touch internally. The sum of their area is 116πcm2 and the distance between their centers is 6cm. Find the radii of the circles.


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a

10 cm, 4 cm

b

6 cm, 12 cm

c

3 cm, 9 cm

d

5 cm, 11 cm 

answer is A.

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Detailed Solution

https://www.vedantu.com/question-sets/dbf47e1f-38ed-4502-bf20-c4b0e61d34163050021009263936416.pngLet the radius of bigger circle be R and smaller be r
πR2+πr2=116π
R2+r2=116→eq(1)
R-r=6
R=6+r
Substituting in eq1
6+r2+r2=116
36+r2+12r+r2=116
r2+6r-40=0
r2+10r-4r-40=0
rr+10-4r+10=0
r+10r-4=0
r=-10 or r=4
Radius of circle cannot be negative so r=4 cm
and, R=6+r=6+4=10 cm
 
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