Answer :

BOC = 2 × BAC


BOC = 2 × 30°


BOC = 60°______________ (i)


OB = OC


OBC = OCB ________________ (ii)


In triangle AOB,


OBC + OCB + BOC = 180°[Sum of angles of triangle]


2 OCB + 60° = 180°


2 OCB = 120°


OCB = 60°


OBC = 60°[From equation (ii)]


From equation (i) and (ii),


OBC = OCB = BOC = 60°


BOC is an equilateral triangle.


OB = OC = BC


Hence, BC is the radius of the circumcircle.


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