    Question

# In the following figure if O is the centre of the circle, AC = 5 cm and BC = 12 cm, then the radius of the circle is A

13 cm

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B

6.5 cm

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C

7.5 cm

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D

12 cm

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Solution

## The correct option is B 6.5 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 right. Therefore angle ACB must be a right angle. Then triangle ACB is a right angled triangle and hence we may apply Pythagoras theorem to this theorem and so obtain the length of the diameter AB. So, AB2=AC2+BC2 ⟹AB2=52+122 ⟹AB2=169 Therefore, AB = 13 cm Therefore the length of the diameter of the circle is 13 cm and hence the length of the radius of the circle is 6.5 cm.  Suggest Corrections  0      Similar questions
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