Question

Find the radius of the circle.

• A. 14 cm
• B. 5 cm
• C. 10 cm
• D. 7 cm

Answer 1

The correct option is C

10 cm

$\angle BOC=2\times 30$

$={60}^{\circ }$ (As angle subtend by an arc at centre is twice the angle subtended by the same arc at the circumference)

Since, OB = OC (radius of the circle)

$\angle OBC=\angle OCB$ ($\Delta BOC$ is an isosceles triangle)

Let, angle $\angle OBC=\angle OCB=x$

So, $x+60+x={180}^{\circ }$

$2x+60=180$

$2x=120$

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

So, $\Delta OBC$ is an equilateral triangle (all the angles are ${60}^{\circ }$)

So, BC = DC = BO = 10 cm

$\therefore$ radius of the circle DC = BO = 10 cm