Question

In the figure , O is the centre of the circle and C is a point on the semi-circle with diameter OA. BC is a tangent through B.

If OB = 1 cm and AB = 3 cm, then $\angle OCB$ = _____

• A. ${60}^{\circ }$
• B. ${45}^{\circ }$
• C. ${30}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

The correct option is C

${30}^{\circ }$

$O{C}^2$ = OB $\times$ OA

$O{C}^2$ = 1 $\times$ 4

OC = 2 cm

sin$\angle COB$ = $\frac{OB}{OC}$ = $\frac{1}{2}$

$\therefore \angle OCB={30}^{\circ }$