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A chord of length $24 cm$ of a circle is at a distance of $5 cm$ from the centre. The radius of the circle is:

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13 cm

12 cm

11 cm

19 cm .

answer is A.

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Detailed Solution

It is given that,
Length of chord, AB = 24 cm.
Distance of chord from the center of circle, OC = 5 cm.
Question Image

As the perpendicular distance from the center bisects the chord.
So, AC = BC
And AC =

\frac{1}{2} AB

\Rightarrow AC = \frac{1}{2} \times 24 cm

\Rightarrow AC = 12 cm

Now, by Pythagoras theorem in triangle ACO, we get,

\Rightarrow {OA}^{2} = {AC}^{2} + {OC}^{2}

\Rightarrow {OA}^{2} = 12^{2} + 5^{2}

\Rightarrow {OA}^{2} = 144 + 25

\Rightarrow {OA}^{2} = 169

\Rightarrow {OA}^{2} = 13^{2}

\Rightarrow OA = 13 cm

.
So, the radius of circle is 13cm.
Hence, the correct option is 1.

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