Question

The length of the minor arc AB of a circle ,centre o is 2 pi cm and the length of the major arc is 22 pi cm. A) find the radius B) the acute angle AOB

Answer 1

Answer:

The value of radius and central angle is not possible  .

Step-by-step explanation:

Given as :

For a circle with center O

The length of the minor arc AB = l = 2 π  centimeter

The length of the major arc AB = L = 22 π  centimeter

Let The radius of the circle = OA = OB = r cm

Let The measure of the angle AOB = Ф

According to question

∵ Length of the arc = $\frac{\Pi \times radius\times \Theta }{180^{\circ}}$

So, The length of minor arc = l = $\dfrac{\Pi \times r\times \Theta }{180^{\circ}}$

Or, 2 π  = $\dfrac{\Pi \times r\times \Theta }{180^{\circ}}$

Or, 2 × 180° = r × Ф            ........A

Again

The length of minor arc = L = $\dfrac{\Pi \times r\times \Theta }{180^{\circ}}$

Or, 22 π = $\dfrac{\Pi \times r\times \Theta }{180^{\circ}}$

Or, 22 × 180° =  r × Ф            ........B

So, from the obtain two equations A and B it is clear that value of radius and central angle can not be determine .

Hence, The value of radius and central angle is not possible  . Answer

Answer 2

Answer:

Radius is 12cm and theta is 30°

Step-by-step explanation:

Circumference = 2 x pi x r

22 pi + 2 pi = 2 x pi x r

24 pi = 2 x pi x r

24 = 2r

12 = r

Find arc length by its formula