Question

If O is the centre of a circle of radius r and AB is a chord of the circle at a distance $\frac{r}{2}$ from O, then $\angle BAO$ =

• A. ${60}^o$
• B. ${45}^o$
• C. ${30}^o$
• D. ${15}^o$

Answer 1

The correct option is C

${30}^o$

r is the radius of the circle with centre O. AB is the chord, at a distance of $\frac{r}{2}$ from the centre.

Let $\angle OAB=\theta$

$sin\theta =\frac{OL}{OA}=\frac{\frac{r}{2}}{r}$

$=\frac{1}{2}=sin{30}^o$

$\therefore \theta ={30}^o$

$\therefore \angle BAO={30}^o$