Confusing math problem?

Question

So my math teacher gave us this problem and I'm having problems trying to figure it out... if anyone knows how to do it, it'd be awesome to know

Two congruent semicricles lie on the diameter of a third semicricl, each tangent to the other two. A small circle in tangent to all three semicircles. If the area of the shaded region is 45pi, what is the length of a radius of the small circle?

So my math teacher gave us this problem and I'm having problems trying to figure it out... if anyone knows how to do it, it'd be awesome to know

Two congruent semicircles lie on the diameter of a third semicircle, each tangent to the other two. A small circle in tangent to all three semicircles. If the area of the shaded region is 45pi, what is the length of a radius of the small circle?

The is a diagram of this problem along with the question here: http://www.brainmass.com/homework-help/math/geometry/8623

to see the diagram click on the Attached help.pdf file

Answer 1

If R is the radius of the third semicircle and r is the radius of the small circle, then
(1/2 pi R^2) - (1/4 pi R^2 + pi r^2) = 45 pi
from this you will get
r = sqrt(R^2 - 180) / 2 for the radius of the small circle.
you need to know the radius of the third semicircle(R) to get r

one possible answer is if R=14 then r=2

Answer 2

The area of the large semicircle = .5pir^2
The area of the two congruent semicircles is pir^2/4
You do not tell us what the shaded region is, which indeed makes the problem confusing.

Answer 3

If 210 are kin and kin of the two the bride and groom, i might subtract that 210 from 330, which components a hundred and twenty. it somewhat is the variety of travellers left to ask who're no longer regarding the two. i might then divide the a hundred and twenty via 2, and that i might say that each and each could invite 60. yet another threat is that because 210 human beings must be seen invitees of the two the bride and the groom, you need to upload 210 to the 60, giving the two components 270 travellers (which includes people who're receiving invites from the two the bride and the groom.) the subject isn't worded ok, and that i think of it particularly is made to trick you. i think of my 2d paragraph is the answer to the trick. If there is no trick meant, it nonetheless isn't nicely-written, yet then 60 may be the respond. pass arranged with the two solutions.

Answer 4

First of all, maybe you should specify where the shaded region is? And if you can you should provide a diagram so people understand you because it is pretty hard to make a mental picture out of this.