The diagram shows a circle centre o. work out the value of a

a = 49°

Step-by-step explanation:

From the figure attached,

In ΔBOC,

OB = OC = Radii of the circle O

Therefore, m∠OBC = m∠OCB = 41° [Opposite angles of the equal sides of a triangle]

By triangle sum theorem,

m∠OBC + m∠OCB + m∠BOC = 180°

41° + 41° + m∠BOC = 180°

m∠BOC = 180° - 82°

              = 98°

Since, "angle subtended by an arc at the center is twice the angle subtended at the circumference",

m∠BOC = 2(m∠BAC)

98° = 2(a)

a = 49°