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 \[\angle POA=120{}^\circ \] |
\[\therefore \] \[\angle POB=180{}^\circ -120{}^\circ =60{}^\circ \] |
\[\because \] \[OP=OB=r\] |
\[\therefore \] \[\angle PBO=\angle OPB\] |
\[=\frac{180{}^\circ -60{}^\circ }{2}=60{}^\circ \] |
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