MCQ

Choose correct alternative answer and fill in the blank.

Length of a chord of a circle is 24 cm. If distance of the chord from the centre is 5 cm, then the radius of that circle is ....

#### Options

12 cm

13 cm

14 cm

15 cm

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#### Solution

Let the chord be AB = 24 cm

Distance of the chord from the centre O is 5 cm.

AO is the radius of the circle.

Perpendicular from the centre of the circle to the chord bisects the chord.

So, AC = CB

In Δ AOC,

OC^{2} + AC^{2} = AO^{2}

⇒ 5^{2} + 12^{2} = AO^{2}

⇒ AO^{2} = 25 + 144 = 169

⇒ AO = 13 cm

Thus, the radius of the circle is 13 cm.

Is there an error in this question or solution?

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