Arcs, length of arc?

Question

http://i10.tinypic.com/2ebacty.png

Using that picture, would anyone be willing to explain to me how to find the measure of Arc CD and the length of it as well.

And also how to find the measure of Arc EF and the length.

I can't seem to figure out how to find the area of CDEF. How can you find the area of it?

Answer 1

The 20° angle is an inscribed angle in the large circle. Its measure is half that of the arc EF that is subtended on the same circle.

So Arc EF = 2*20 = 40°
Since the radius of the large circle is 5 the length of arc EF is:
Length Arc EF = 2πr(40/360) = 2π5(1/9) = 10π/9
___________

Arc AB on the smaller circle is given to be 35°.
The measure of an exterior angle that intercepts a circle twice is half the difference of the two subtended arcs.

Angle = (1/2)(CD - AB)
20° = (1/2)(CD - 35°)
40° = CD - 35°
75° = CD
CD = 75°

Since the radius of the small circle is 2 the length of arc CD is:
Length Arc CD = 2πr(75/360) = 2π2(75/360) = 5π/6