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
• B. 6.5 cm
• C. 7.5 cm
• D. 12 cm

Answer 1

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, $A{B}^2=A{C}^2+B{C}^2$

$⟹A{B}^2=5^2+{12}^2$

$⟹A{B}^2=169$

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.