question_answer

If an equilateral \[\Delta ABC\]is inscribed in a circle with centre at O, then \[\angle BOC,\]\[\angle COA\]and \[\angle AOB\]are respectively                                [SSC (CGL) 2014]

A) \[50{}^\circ ,\]\[60{}^\circ ,\]\[70{}^\circ \]      

B) \[120{}^\circ ,\]\[120{}^\circ ,\]\[120{}^\circ \]

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

D) \[80{}^\circ ,\]\[120{}^\circ ,\]\[160{}^\circ \]

Correct Answer: B

Solution :

Since, given ABC is an equilateral triangle.

So, angle formed by incentre is also equal.

\[\therefore \]\[\angle BOC,\]\[\angle COA\]and \[\angle AOB\]are equal to \[120{}^\circ .\]