A circle can have ______ parallel tangents at the most.

two

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zero

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four

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Infinite number of a set of

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Solution

The correct option is D Infinite number of a set of
$L e t A B & C D b e t w o p a r a l l e l t a n g e n t s t o a c i r c l e w i t h c e n t r e O a t P & Q r e s p e c t i v e l y . T h e n P Q i s a d i a m e t e r o f t h e c i r c l e s i n c e O P ⊥ A B & O Q ⊥ C D . (t h e r a d i u s, p a s s i n g t h r o u g h t h e p o i n t o f c o n t a c t o f a t a n g e n t t o a c i r c l e, i s p e r p e n d i c u l a r t o t h e t a n g e n t) . B u t t h e r e a r e i n f i n i t e n u m b e r o f d i a m e t e r s o f a c i r c l e . S o t h e r e a r e i n f i n i t e n u m b e r o f a s e t o f t w o p a r a l l e l t a n g e n t s t o a c i r c l e . A n s - O p t i o n D .$

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