Question

a b c d e f g h a regular octagon inscribed in a circle of radius 1 cm o is the centre of the circle find angle aob length of Chord ab and length of Arc ab​

Answer 1

Answer:

Angle AOB = 45° or π/4 rad

Length of Chord AB = √2 cm = 1.414 cm

Length of Arc AB = 0.785 cm

Step-by-step explanation:

Given Data:

ABCDEFGH is a regular octagon.

Radius of the circle, R = 1 cm

To find:angle AOB, length of chord ab and length of arc

Step 1: finding ∠AOB

In regular octagon, n = 8

Since ABCDEFGH is a regular octagon, therefore, the centre angle is given as,

θ = ∠AOB = 360° / 8  = 45° = 45° * π/180° = π/4 rad

Step 2: finding the length of chord AB

R = OA = OB = 1cm

Consider ∆AOB(from figure given below), by using Pythagoras theorem, we get

Length AB = $\sqrt{OA^2 + OB^2}$ = $\sqrt{1^2 + 1^2}$ = √2 cm

Step 3: finding the length of arc AB

If θ is measured in radians then the arc length of AB i.e., “s” is given as,

s = r * θ = 1 cm * π/4 rad = 0.785 cm