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What will be the radius of the circle if a chord of a length 30 cm is drawn at a distance of 8 cm from the center of a circle?

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20cm

17cm

19cm

25cm

answer is B.

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Detailed Solution

It is given that a chord of a length 30 cm is drawn at a distance of 8 cm from the center of a circle.
We have to find the radius.
Using the Pythagoras Theorem:

c 2 = a 2 + b 2

Where, c=hypotenuse, a = perpendicular and b=base.
Suppose AB is a chord of the circle.
Question Image

We know that the perpendicular from the centre of a circle to a chord bisects the chord.

A L = 12 A B = 12 (30) = 15 c m

For right -angled

OLA, using Pythagoras Theorem,

O A 2 = A L 2 + O L 2 ⇒ O A 2 = 152 + 82 ⇒ OA= 289 ⇒ O A = 17 c m

So, the radius of the circle is 17cm.
Therefore, option 2 is correct.

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