# two circles touch internally.the sum of their areas is 116cm and the distance between their centers is 6cm.find the radii of the circles.

### Asked by prabinbinu2001 | 3rd Apr, 2017, 11:14: PM

Expert Answer:

###
Let the radius of 2 circles be r1 and r2
Sum of area = 116π
π(r1)^{2} + π(r2)^{2} = 116π
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 = 4 cm and r1 = 10 cm

Let the radius of 2 circles be r1 and r2

Sum of area = 116π

π(r1)

^{2}+ π(r2)^{2}= 116πi.e. (r1)

^{2 }+ (r2)^{2 }= 116Also, r1 - r2 = 6

r1 = 6+r2

Substituting it back in the above equation

(6+r2)

^{2 }+ (r2)^{2 }= 1162(r2)

^{2}+ 12r2 + 36 = 1162(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 = 4 cm and r1 = 10 cm

### Answered by Rebecca Fernandes | 29th Nov, 2017, 02:26: PM

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