Question

In the given figure if AB = 5cm and BC = 12 cm then the radius of the circle is ___

• A. 12 cm
• B. 5 cm
• C. Both a and b
• D. Can't be found

Answer 1

The correct option is B

5 cm

Given $\angle ACB={30}^{\circ }$ and BA = 5 cm, BC = 12 cm

Join O and A, O and B

Now $\angle AOB=2\times \angle ACB$

($\because$ The angle subtends by arc at centre is twice that it subtends at any point on the remaining part of ccircumference)

$\therefore \angle AOB={60}^{\circ }$

NOw $\because OA=OB$

$\therefore \angle ABO=\angle BAO$

Let $\angle ABO=x$

$\Rightarrow x+x+{60}^{\circ }={180}^{\circ }$

$\therefore x={60}^{\circ }$

$\therefore \Delta AOB$ is equilateral triangle.

$\therefore OA=5cm$

= Radius of circle