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

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Senior Manager
Joined: 14 Apr 2005
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Location: India, Chennai
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O is the centre of a semicircle on AB as diameter. We also [#permalink]  05 Jan 2006, 03:31
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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.
VP
Joined: 21 Sep 2003
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[#permalink]  05 Jan 2006, 03:56
A?

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

=> 18r = 36
=> r = 2

See attached picture. (Now it is really attached)
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circles.doc [28.5 KiB]

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Last edited by giddi77 on 05 Jan 2006, 04:15, edited 1 time in total.
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[#permalink]  05 Jan 2006, 04:11
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)
Senior Manager
Joined: 14 Apr 2005
Posts: 419
Location: India, Chennai
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[#permalink]  05 Jan 2006, 23:51
Good solutions Giddi and BG. The OA is A.
[#permalink] 05 Jan 2006, 23:51
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# O is the centre of a semicircle on AB as diameter. We also

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