If chord PQ of a circle have length equal to the radius then the distance of chord from centre in terms of radius is

\frac{\sqrt{3}}{4} r

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\frac{\sqrt{5}}{2} r

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\frac{3 \sqrt{3}}{2} r

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\frac{\sqrt{3}}{2} r

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Solution

The correct option is D $\frac{\sqrt{3}}{2} r$
$G i v e n - P Q i s a c h o r d o f a c i r c l e w i t h c e n t r e O s u c h t h a t O P = O Q = r = P Q w h e n r i s t h e r a d i u s o f t h e c i r c l e . T o f i n d o u t h = O N, t h e d i s t a n c e o f P Q f r o m O . S o l u t i o n - Δ O P Q i s e q u i l a t e r a l s i n c e a l l i t s s i d e s = r . N o w h e i g h t o f a n e q u i l a t e r a l t r i a n g l e w i t h s i d e = a i s \frac{\sqrt{3}}{2} a a n d i t b i s e c t s t h e b a s e a t r i g h t a n g l e . H e r e a = r . ∴ T h e h e i g h t = O N = h = \frac{\sqrt{3}}{2} r . = B u t O N i s t h e d i s t a n c e o f t h e c h o r d P Q f r o m O s i n c e t h e p e r p e d i c u l a r d i s t a n c e o f a c h o r d f r o m t h e c e n t r e b i s e c t s t h e c h o r d a t r i g h t a n g l e . S o h = O N = \frac{\sqrt{3}}{2} r i s t h e d i s t a n c e o f t h e c h o r d P Q f r o m O . A n s - O p t i o n D .$

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