# A circle with cen

Given: and

Consider ΔOAB

Here,

OBA = OAB = 30° (angles opposite to equal sides are equal)

Similarly, in ΔAOC

OCA = OAC = 40° (angles opposite to equal sides are equal)

Here,

CAB = OAB + OAC = 30° + 40° = 70°

Here,

CAB = BOC (The angle subtended by an arc at the center is twice the angle subtended by the same arc on any point on the remaining part of the circle).

CAB = BOC

2×70° = BOC

BOC = 140°.

BOC = 140

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