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The radius of a circle is 13 cm and the ...

The radius of a circle is `13` cm and the length of one of its chords is `10` cm . The distance of the chord from the centre is

A

`11.5 cm`

B

`12 cm`

C

`sqrt(69)` cm

D

`23 cm`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `O` be the centre of acircle with radius `OA = 13 cm`
Let AB be the chord of length `10 cm`. Draw OL `_|_` AB.
Then, L is the midpoint of AB. Thus, ALA `= 5` cm
`OL^(2) = OA^(2) -AL^(2) = (13)^(2) - (5)^(2) = 169-25 = 144`
`implies OL = sqrt(1 44) = 12 cm`

Distance of the chord from the centre `= 12 cm`.
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