Question

If the angle between two tangents drawn from an external point \( P \) to a circle of radius 3 cm and centre \( O \) is \( 60^\circ \), find the length of \( OP \).

Hint:

Length of OP in Circle: Use \( OP = \frac{r}{\cos (\theta/2)} \).

Answer 1

Using the formula: \[ OP = \frac{r}{\cos \frac{\theta}{2}} \] \[ OP = \frac{3}{\cos 30^\circ} \] \[ = \frac{3}{\frac{\sqrt{3}}{2}} = \frac{6}{\sqrt{3}} = 6 \, \text{cm} \] Thus, the length of \( OP \) is \( \mathbf{6 \, \text{cm}} \). Correct Answer: \( 6 \, \text{cm} \)