Question

In the given figure, O is the centre of a circle, AB is a side of regular octagon and AC is a side of regular hexagon. Find :
(i) ∠AOB (ii) ∠AOC (iii) ∠BOC.

Answer 1

Answer:

∠AOB = 60°, ∠BOC = 45° , ∠ABC = 105°, ∠ACB = 30°

Step-by-step explanation:

Regular hexagon which is inscribed in circle, will have sides equal to radius (r) of circle.

∴ AB = OA = OB = OC = r

Δ AOB is equilateral triangle.

∴ ∠AOB = 60°

BC is a side of octagon,

∴ ∠BOC = 360 / 8 = 45°

∠BAC = ∠BOC / 2 = 45/2 = 22.5°  Reason - Angle subtended in arc is twice the angle subtended at circumference.

∠ACB = ∠BOA / 2 = 60/2 = 30° Reason - Angle subtended in arc is twice the angle subtended at circumference.

∠ABC = ∠ABO + ∠OBC = 60° + 45° = 105°