Two equal chords, $A B$ and $C D$ are at a distance of 10 cm from each other. Find the distance of chord $A B$ from the centre.

$6 c m$

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$5 c m$

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$20 c m$

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$12 c m$

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Solution

The correct option is B
$5 c m$

Consider the figure:

$A B = C D$ [Given]

$E F = 10 c m$

We know that equal chords are equidistant from the centre.

So, $O E = O F$

$E F = O E + O F$

$\Rightarrow 2 O E = 10$

$\Rightarrow O E = O F = 5 c m$

So, both the chords, $A B$ and $C D$ are equidistant from the centre and is at a distance of 5 cm.

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