A circle with centre O is given in which ∠OBA = 30° and ∠OCA = 40°. Find ∠BOC.

Question

A circle with centre O is given in which ∠ OBA = 30° and ∠ OCA = 40°. Find ∠ BOC.

Philoid · Accepted Answer

Given: and

Consider ΔOAB

Here,

OA = OB (radius)

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

Similarly, in ΔAOC

OA = OC (radius)

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

Here,

∠CAB = ∠OAB + ∠OAC = 30° + 40° = 70°

Here,

2×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).

2×CAB = BOC

2×70° = BOC

BOC = 140°.

BOC = 140