Draw different pairs of circles. How many points does each pair have in common ? The maximum number of common point/points is/are

2

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1

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infinite

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0

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Open in App

Solution

The correct option is C infinite
$S o l u t i o n - W e d r a w p a i r s o f c i r c l e s s o t h a t (i) T h e d i s t a n c e b e t w e e n t h e c e n t r e s > t h e s u m o f t h e i r r a d i i, (i i) T h e d i s t a n c e b e t w e e n t h e c e n t r e s = t h e s u m o f t h e i r r a d i i, (i i) T h e d i s t a n c e b e t w e e n t h e c e n t r e s < t h e s u m o f t h e i r r a d i i, (i i) T h e d i s t a n c e b e t w e e n t h e c e n t r e s = 0 T a k e (a) d i f f e r e t r a d i i (b) e q u a l r a d i i . I n f i g I T h e d i s t a n c e b e t w e e n t h e c e n t r e s > t h e s u m o f t h e i r r a d i i, ⟶ N o c o m m o n p o i n t . I n f i g I I T h e d i s t a n c e b e t w e e n t h e c e n t r e s = t h e s u m o f t h e i r r a d i i, ⟶ O n e c o m m o n p o i n t . I n f i g I I I T h e d i s t a n c e b e t w e e n t h e c e n t r e s < t h e s u m o f t h e i r r a d i i, ⟶ T w o c o m m o n p o i n t s . I n f i g I V a T h e d i s t a n c e b e t w e e n t h e c e n t r e s = 0 a n d t h e r a d i i a r e d i f f e r e n t . ⟶ N o c o m m o n p o i n t . I n f i g I V b T h e d i s t a n c e b e t w e e n t h e c e n t r e s = 0 a n d r a d i i a r e e q u a l . T h e c i r c l e s w i l l c o i n c i d e . ⟶ I n f i n i t e n u m b e r o f c o m m o n p o i n t s . A n s - O p t i o n C,$

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