question_answer

AB is a diameter of a circle having centre at O. P is a point on the circumference of the circle. If \[\angle POA=120{}^\circ ,\] then measure of \[\angle PBO\] is                                                                                                                   [SSC (10+2) 2015]

A) \[68{}^\circ \]                          

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

C) \[75{}^\circ \]              

D) \[70{}^\circ \]

Correct Answer: B

Solution :

Given, AB is diameter

and \[\angle POA=120{}^\circ \]

\[\therefore \]      \[\angle POB=180{}^\circ -120{}^\circ =60{}^\circ \]

\[\because \]       \[OP=OB=r\]

\[\therefore \]      \[\angle PBO=\angle OPB\]

\[=\frac{180{}^\circ -60{}^\circ }{2}=60{}^\circ \]