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
• B. 3 cm
• C. 5 cm
• D. 12 cm

Answer 1

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

$⟹A{B}^2=3^2+4^2$

$⟹A{B}^2=25$

Therefore, AB = 5 cm

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