Question

In figure 3.56, in a circle with centre O,length of chord AB is equal to the radius of the circle. Find measure of each of the following.
(1) ∠AOB
(2)∠ACB
(3) arcAB
(4) arcACB.

Answer 1

Given that, OA = OB = AB
Therefore, triangle OAB is equilateral triangle
Therefor,angle AOB =60°
Now, angle ACB = angle AOB/2
=. 60/2 = 30°
Now, arc AB= (60/360) × 2×22/7 × r

And arc ACB =. 2*22/7*r - arc AB

Answer 2

Answer:

Step-by-step explanation:

OA = OB = AB = Radius

Δ AOB is an equilateral triangle

so ∠AOB = 60°

∠ACB = (1/2) ∠AOB = (1/2) * 60° = 30°

Arc AB = (60/360) * 2 π * Radius

= (1/6) 2π * Radius

Arc ACB = 2π * Radius - (1/6) 2π * Radius

=>Arc ACB =  2π * Radius ( 1 - 1/6)

=>Arc ACB =  2π * Radius ( 5/6)

=>Arc ACB =  (5/6) 2π * Radius