if OA= 3 & AB= 2 what is the ratio of the circumference of the smaller circle to the circumference of the larger circle

(B) 3/5

Step-by-step explanation:

In the figure above, both circles have their centers at point O. Point A lies on segment OB. If OA = 3 and AB = 2, what is the ratio of the circumference of the smaller circle to the circumference of the larger circle?

(A) 2/3

(B) 3/5

(C) 9/16

(D) 1/2

(E) 4/9

The circumference of a circle is the perimeter of the circle, that is it is the arc length of the circle. The circumference of a circle is given as:

Circumference = 2 π r.   Where r is the radius of the circle.

The radius of the bigger circle = length of OB = OA + AB = 3 + 2 = 5

Circumference of the bigger circle = 2 π (5) = 10π

The radius of the smaller circle = length of OA = 3

Circumference of the smaller circle = 2 π (3) = 6π

The ratio of the circumference of the smaller circle to the circumference of the larger circle = circumference of the smaller circle / circumference of the larger circle = 6π / 10π = 3/5