Question

In the given figure of circle with centre O, chord AB makes an angle of \(80^\circ\) with the centre. Then \(\angle APB\) is

• A. \(40^\circ\)
• B. \(100^\circ\)
• C. \(140^\circ\)
• D. \(90^\circ\)

Hint:

In a circle, the angle subtended by a chord at the centre is twice the angle subtended at any point on the remaining part of the circle.

Answer 1

The Correct Option is A

The angle \(\angle APB\) at the circumference of the circle is half of the angle at the centre, i.e., \[ \angle APB = \frac{1}{2} \times \angle AOB = \frac{1}{2} \times 80^\circ = 40^\circ \] Thus, the correct answer is \(40^\circ\).