Two circles which are not congruent touch externally- The sum of their areas is 130- cm 2 and the distance between their centres is 14 cm- The sum of radii of the circles is

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Two Circles Touching Internally and Externally

Two circles w...

Question

Two circles which are not congruent touch externally. The sum of their areas is ${130 π c m}^{2}$ and the distance between their centres is $14 c m$ . The sum of radii of the circles is

14 c m

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21 c m

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7 c m

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28 c m

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Solution

The correct option is A $14 c m$
$G i v e n - P & Q a r e t h e c e t r e s o f t w o c i r c l e s o f r a d i u s r_{1} & r_{2} r e s p e c t i v e l y, t o u c h i n g e a c h o t h e r a t M . P Q = 14 c m . T o f i n d o u t - t h e s u m o f t h e i r r a d i i = ? S o l u t i o n - W e d r a w t h e c o m m o n t a n g e n t A B a t M . i . e P M = r_{1} & Q M = r_{2} . N o w ∠ A M P = 90^{o} b e c a u s e i f a l i n e t o u c h e s a c i r c l e a t a p o i n t t h e n t h e r a d i u s t h r o u g h t h a t p o i n t i s p e r p e n d i c u l a r t o t h e t a n g e n t a t t h a t p o i n t . S i m i l a r l y ∠ A M Q = 90^{o} . S o ∠ A M P + ∠ A M Q = 90^{o} + 90^{o} = 180^{o} . ∴ ∠ A M P & ∠ A M Q a r e l i n e a r p a i r . S o P M & Q M a r e o n t h e s a m e s t r a i g h t l i n e . ∴ T h e d i s t a n c e b e t w e e n t h e c e n t r e s P & Q i s P Q = P M + Q M = r_{1} + r_{2} . B u t P Q = 14 c m (g i v e n) . ∴ r_{1} + r_{2} = 14 c m . A n s - O p t i o n A .$

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Two circles which are not congruent touch externally. The sum of their areas is 130πcm2 and the distance between their centres is 14cm. The sum of radii of the circles is

Two circles which are not congruent touch externally. The sum of their areas is ${130 π c m}^{2}$ and the distance between their centres is $14 c m$ . The sum of radii of the circles is