A circle of radius $25$ units has a chord going through a point that is located $10$ units from the centre. What is the shortest possible length that chord could have ?

25

units

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\sqrt{525}

units

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40

units

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\sqrt{2100}

units

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Solution

The correct option is D $\sqrt{2100}$ units
$T h e c h o r d l e n g t h f o r a c i r c l e o f r a d i u s r a n d p e r p e n d i c u l a r d i s t a n c e, d, f r o m t h e c h o r d t o t h e c e n t e r o f t h e c i r c l e i s B y P y t h a g o r e a s t h e o r m l = 2. \sqrt{r^{2} - d^{2}} r = 25 c m a n d d = 10 c m (G i v e n) \Rightarrow C h o r d l e n g t h 2. \sqrt{25^{2} - 10^{2}} u n i t s = 2. \sqrt{625 - 100} = \sqrt{4.525} = \sqrt{2100} u n i t s H e n c e o p t i o n (D) i s r i g h t a n s w e r$

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A circle of radius 25 units has a chord going through a point that is located 10 units from the centre. What is the shortest possible length that chord could have ?

The correct option is D √2100 unitsThechordlengthforacircleofradiusrandperpendiculardistance,d,fromthechordtothecenterofthecircleisByPythagoreastheorml=2.√r2−d2r=25cmandd=10cm(Given)⇒Chordlength2.√252−102units=2.√625−100=√4.525=√2100unitsHenceoption(D)isrightanswer

A circle of radius $25$ units has a chord going through a point that is located $10$ units from the centre. What is the shortest possible length that chord could have ?