Question

In the given figure, PA and PB are tangents to a circle centred at O. If \( \angle AOB = 130^\circ \), then \( \angle APB \) is equal to :

• A. \( 130^\circ \)
• B. \( 50^\circ \)
• C. \( 120^\circ \)
• D. \( 90^\circ \)

Hint:

Just subtract the central angle from 180 to find the angle between tangents.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The angle between the tangents from an external point is supplementary to the angle subtended by the radii at the centre.
Step 2: Detailed Explanation:
In quadrilateral OAPB:
\( \angle OAP = 90^\circ \) and \( \angle OBP = 90^\circ \).
The sum of angles in a quadrilateral is \( 360^\circ \).
\[ \angle APB + \angle AOB = 180^\circ \]
\[ \angle APB + 130^\circ = 180^\circ \]
\[ \angle APB = 50^\circ \]
Step 3: Final Answer:
\( \angle APB = 50^\circ \).