question_answer

AB is the diameter of a circle with centre O and P is a point on it. If \[\angle POA=120{}^\circ ,\]then the value of \[\angle PBO\]is

A) \[30{}^\circ \]

B) \[50{}^\circ \]

C) \[60{}^\circ \]

D) \[40{}^\circ \]

Correct Answer: C

Solution :

[c] The angle subtended by an arc at the centre is double the angle substended by the same arc at  The circumference of circle, \[\therefore \]      \[\angle POB=\frac{1}{2}\times \angle POA=\frac{1}{2}\times 120{}^\circ \] \[=60{}^\circ \]