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Question
In the given figure, AB is a side of a regular six-sided polygon and AC is a side of a regular eight-sided polygon inscribed in the circle with centre O. Calculate the sizes of:
- ∠AOB,
- ∠ACB,
- ∠ABC.
Solution
i. Arc AB subtends ∠AOB at the centre and ∠ACB at the remaining part of the circle.
∴ `∠ACB = 1/2∠AOB`
Since AB is the side of a regular hexagon,
∠AOB = 60°
ii. `∠AOB = 60^circ => ∠ACB = 1/2 xx 60^circ = 30^circ`
iii. Since AC is the side of a regular octagon,
`∠AOC = 360^circ/8 = 45^circ`
Again, Arc AC subtends ∠AOC at the center and ∠ABC at the remaining part of the circle.
`=> ∠ABC = 1/2 ∠AOC`
`=> ∠ABC = 45^circ/2 = 22.5^circ`
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