Question

If \( TP \) and \( TQ \) are two tangents drawn from an external point \( T \) to a circle whose centre is \( O \) such that \( \angle POQ = 120^\circ \), then the value of \( \angle OTP \) is:

• A. \( 40^\circ \)
• B. \( 30^\circ \)
• C. \( 50^\circ \)
• D. \( 60^\circ \)

Hint:

For two tangents drawn from an external point, the angle between them is: \[ \frac{180^\circ - \text{Angle at Centre}}{2}. \]

Answer 1

The Correct Option is B

The angle subtended by two tangents at the external point is given by:
\[ \angle OTP = \frac{180^\circ - \angle POQ}{2}. \] \[ \angle OTP = \frac{180^\circ - 120^\circ}{2} = \frac{60^\circ}{2} = 30^\circ. \]