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A chord of a circle of radius 10 cm subtends a right angle at its center. Find out the length of the chord (in cm).

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5 \sqrt{2} cm

10 \sqrt{2} cm

\frac{5}{3} cm

10 \sqrt{3} cm

answer is B.

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Detailed Solution

It is given that a chord of a circle of radius 10 cm subtends a right angle at its center.
Then, consider a circle with a centre at O, radius 10 cm. AB is the chord that subtends

90 °

at its center.
Question Image

Now, using Pythagoras theorem in

△ OAB

O A^{2} + O B^{2} = A B^{2}

10^{2} + 10^{2} = A B^{2}

A B^{2} = 200

AB = 10 \sqrt{2}

Therefore, length of the chord is

10 \sqrt{2} cm

.
Hence, option (2) is correct.

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