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: (I) ∠Aob, - Mathematics

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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:
(i) ∠AOB,  (ii) ∠ACB  (iii) ∠ABC

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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° ⇒ ∠ACB = 1/2 xx60° = 30°`

(iii) Since AC is the side of a regulare octagon,
       `∠AOC = (360°) /8= 45°`

Again, Arc AC subtends ∠AOC at the center and
∠ABC at the remaining part of the circle.
⇒ `∠ABC = 1/2 ∠AOC`

⇒ `∠ABC = (45°)/2 = 22.5°`

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Chapter 17: Circles - Exercise 17 (B) [Page 265]

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Selina Concise Maths Class 10 ICSE
Chapter 17 Circles
Exercise 17 (B) | Q 5 | Page 265

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