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