Can we draw a chord of 11cm in the circle of radius 5cm? Explain your answer:

Yes

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Cannot be determined

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Options B & D

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No.

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Solution

The correct option is D No.
$G i v e n - r = 5 c m i s t h e r a d i u s o f a c i r c l e a n d A B i s a c h o r d o f t h e s a m e c i r c l e . (f i g 1) T o f i n d o u t - i f i t i s p o s s i b l e t h a t A B = 11 c m . S o l u t i o n - H e r e t h e r a d i u s r - 5 c m . ∴ T h e d i a m e t e r o f t h e c i r c l e = D = 2 \times r = 2 \times 5 c m = 10 c m . W e k n o w t h a t d i a m e t e r i s t h e g r e a t e s t c h o r d . ∴ D s h o u l d b e > A B . . . . . . . . (i) B u t A B = 11 c m . i . e A B > D . i . e i f t h e p o i n t A i s o n t h e c i r c l e t h e n t h e p o i n t B w i l l b e i n t h e e x t e r i o r o f t h e c i r c l e . (f i g 2) T h i s c o n t r a d i c t s t h e r u l e (i) . S o, i n t h i s c a s e, t h e l e n g t h o f t h e c h o r d = 11 c m, i s i m p o s s i b l e . A n s - O p t i o n D .$

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