The radius of a circle with centre O is 7 cm, OP $=$ 4 cm and OQ $=$ 9 cm state with reason which point lies in the interior and which in the exterior of the circle.

T h e p o i n t Q i s i n t h e i n t e r i o r a n d t h e p o i n t P i s i n t h e e x t e r i o r o f t h e c i r c l e .

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T h e p o i n t P i s i n t h e i n t e r i o r a n d t h e p o i n t Q i s i n t h e e x t e r i o r o f t h e c i r c l e .

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T h e p o i n t P i s i n t h e e x t e r i o r a n d t h e p o i n t Q i s i n t h e e x t e r i o r o f t h e c i r c l e .

No worries! We‘ve got your back. Try BYJU‘S free classes today!

T h e p o i n t P i s i n t h e i n t e r i o r a n d t h e p o i n t Q i s i n t h e i n t e r i o r o f t h e c i r c l e .

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Solution

The correct option is C $T h e p o i n t P i s i n t h e i n t e r i o r a n d t h e p o i n t Q i s i n t h e e x t e r i o r o f t h e c i r c l e .$
$G i v e n - O A i s t h e r a d i u s r = 7 c m o f a c i r c l e w i t h c e n t r e O . P & Q a r e t w q p o i n t s s u c h t h a t d (O P) = 4 c m a n d d (O Q) = 9 c m . T o f i n d o u t - T h e p o s i t i o n s o f P & Q . S o l u t i o n - W e k n o w t h a t i f a p o i n t i s a t a d i s t a n c e d f r o m t h e c e n t e r o f a c i r c l e o f r a d i u s r, t h e n (i) t h e p o i n t i s i n t h e e x t e r i o r o f t h e c i r c l e i f r < d . . . . . . . . . . (i) a n d (i i) t h e p o i n t i s i n t h e i n t e r i o r o f t h e c i r c l e i f r > d . . . . . . . . . (i i) H e r e r = 7 c m a n d d (O P) = 4 c m . ∴ r > d (O P) . i . e b y (i i) P i s i n t h e i n t e r i o r o f t h e c i r c l e . A g a i n d (O Q) = 9 c m . ∴ r < d (O Q) . i . e Q i s i n t h e e x t e r i o r o f t h e c i r c l e . S o t h e p o i n t P i s i n t h e i n t e r i o r a n d t h e p o i n t Q i s i n t h e e x t e r i o r o f t h e c i r c l e . A n s - O p t i o n B .$

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