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O is the centre of a semicircle on AB as diameter. We also

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O is the centre of a semicircle on AB as diameter. We also [#permalink] New post 05 Jan 2006, 04:31
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O is the centre of a semicircle on AB as diameter. We also have a semicircle on OA and OB. (i.e the semicircles on OA and OB are inscribed within the semicircle on AB as diameter). Now A circle with centre C is drawn to touch this semicircle and also other semicircles drawn on OA & OB as diameters. Find the radius of circle with centre C if OA = 6.


(1) 2

(2) 3

(3) 3.5

(4) 4

I do not have the OA answer for this question.
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 [#permalink] New post 05 Jan 2006, 04:56
A?

(r+3)^2 = (6-r)^2 + 3^2

=> 18r = 36
=> r = 2

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Last edited by giddi77 on 05 Jan 2006, 05:15, edited 1 time in total.
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 [#permalink] New post 05 Jan 2006, 05:11
I used some sort of imagination . The area of the biggest semicircle is (36pi)/2 or 18pi. The area of both smaller semicirles together is 9pi.Then the area outside the smaller semicircles within the bigger one is 18pi-9pi or 9pi. So the radius of the circle inscribed is <3 only option A)
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 [#permalink] New post 06 Jan 2006, 00:51
Good solutions Giddi and BG. The OA is A.
  [#permalink] 06 Jan 2006, 00:51
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