circles, arc and area. please help T.T

[gd439]

I really don't know how to do this question. I'm guessing the two circles form a rectangle but I don't exactly know why..
Can you please help? I really appreciate it!!

 

[gd439]

thank you for the hint. I figured out until that stage. But I don't know how to find the length of arc AM and arc BM.
Is it one quarter of the perimeter of the small circle each?

 

[gd439]

Thank you for the hint. My main concern is the arc AM and arc BM. I don't know how to find the length. I'm guessing each length is one quarter of the perimeter but I don't know why?

Well, somewhat difficult to help you: diagram not labelled...
plus you didn't indicate where you're stuck...

Here's a hint:
label the 2 tangent points A and B
(where the 2 inner circles touch the larger circle).
Draw lines AB, OA and OB : triangle OAB is equilateral.
And AB = 15, of course.

Make M the tangent point where 2 inner circles touch.
Then perimeter of shaded region is arcAM + arcBM + arcAB

Good luck. Sorry, we don't give a-la-carte solutions.

 

[gd439]

working

This is my working, but I can't get 11and2/3 pi as perimeter.. which is what the answer is supposed to be. I thought about this for more than one hour and I still can't figure out. can you please help me?