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 of the chord?

25 u n i t s

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\sqrt{525} u n i t s

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40 u n i t s

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\sqrt{2100} u n i t s

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Solution

The correct option is B $\sqrt{2100} u n i t s$
For length of shortest chord we move in direction $⊥$ to the length of chord .
From $Δ A O C$ $A C = \sqrt{25^{2} - 10^{2}} = \sqrt{525}$ units
As $O A = O B$ and $∠ O C B = ∠ O C A = 90^{\circ}$ ( $O C$ common)
$∴ Δ O A C ≃ Δ O C B$
$\Rightarrow A C = B C$
$\Rightarrow A B =$ length of chord $= 2 A C = 2 \sqrt{525} = \sqrt{2100}$ units

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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 of the chord?

The correct option is B √2100 unitsFor length of shortest chord we move in direction ⊥ to the length of chord . From ΔAOC AC=√252−102=√525 units As OA=OB and ∠OCB=∠OCA=90∘ (OC common) ∴ΔOAC≃ΔOCB⇒AC=BC ⇒AB= length of chord =2AC=2√525=√2100units

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 of the chord?