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Question

In the following figure if O is the centre of the circle, AC = 3 cm and BC = 4 cm, then the length of the diameter of the circle is


A

4 cm

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B

3 cm

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C

5 cm

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D

12 cm

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Solution

The correct option is C

5 cm


Given O is the centre of the circle. Then AB must be the diameter of the circle.

We know that angle in a semicircle is 90°

Therefore angle ACB is a right angle.

Then triangle ACB is a right angled triangle and hence we may apply Pythagoras theorem to this triangle and so obtain the length of the diameter AB.

So, AB2=AC2+BC2

AB2=32+42

AB2=25

Therefore, AB = 5 cm

Therefore the length of the diameter of the circle is 5 cm.


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