Question

In the given figure , 'o' is the centre of the circle and the length of arc AB is twice the length of arc BC . If angle AOB = 104° , find by giving reasons : angle BOC , OAC, and angle BAC​

Answer 1

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Step-by-step explanation:

Answer 2

In the given figure , 'o' is the centre of the circle and the length of arc AB is twice the length of arc BC .

As we know that, the measure of inscribed angle is half the measure of its intercepted arc.

So, we have,

∠ = 1/2 (m arc)

Given,

AB = 2 × BC

∠ AOB = 104°

Now consider,

∠ AOB = 1/2 (m arc AB)

104° = 1/2 (m arc AB)

∴ AB = 208°

BC = AB/2 = 208°/2

∴ BC = 104°

∠ BOC  = 1/2 (m arc BC)

= 1/2 × 104°

= 52°

∴ ∠ BOC = 52° ...........(i)

∠ BAC = 1/2 ∠ BOC

= 1/2 × 52°

= 26°

∴ ∠ BAC = 26° ...........(iii)

∠ AOC = ∠ AOB + ∠ BOC

= 104° + 52°

∴ ∠ AOC = 156°

as angles opposite to equal sides are equal, we have,

∠ OAC = ∠ OCA

Now, in Δ AOC,

∠ OAC + ∠ OCA + ∠ AOC = 180°

∠ OAC + ∠ OAC + 156° = 180°

2 ∠ OAC = 180° - 156°

2 ∠ OAC = 24°

∴ ∠ OAC = 12° ..............(ii)