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 \(\angle APB\) on the circle's circumference is half the angle at the center. Therefore, \[ \angle APB = \frac{1}{2} \times \angle AOB = \frac{1}{2} \times 80^\circ = 40^\circ \] The correct answer is thus \(40^\circ\).