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# inscribed circle in half circle

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Intern
Joined: 16 Apr 2010
Posts: 36
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inscribed circle in half circle [#permalink]  30 Aug 2010, 07:21
00:00

Difficulty:

55% (hard)

Question Stats:

44% (01:54) correct 56% (01:18) wrong based on 16 sessions
A circle is inscribed in a half circle with a diameter of $$\pi$$ . What is the ratio of the area of the half circle to the area not covered by the inscribed circle?

a, 1:1

b, 1:2

c, 1:4

d, 3:4

e, 2:1

the official answer say that the diameter of inscribed circle is $$\pi$$/2.

I wonder how do we know the diameter of inscribed circle is $$\pi$$/2.

Through research in the internet, there are many situations in which a circle inscribed other, but there diameter is not relating to each other.

Help me to find out what is wrong with my thought.
[Reveal] Spoiler: OA
Manager
Joined: 07 Oct 2006
Posts: 73
Location: India
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Kudos [?]: 8 [0], given: 3

Re: inscribed circle in half circle [#permalink]  30 Aug 2010, 07:56
Hi bupbebeo,

I also agree with your thoughts. It is not mandatory for the inscribed circle to have diameter as half of the diameter of the outer half circle. But, if you look at the closer look at the answer choices, you can conclude that we can have only one answer as 2:1. The answer should be >= 2:1. There is only one option which satisfies the condition. Hence, we have to pick the option. If GMAT gives another option which has value > 2, then we can have an argument. But, this one is straight forward, I presume.

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Intern
Joined: 16 Apr 2010
Posts: 36
Followers: 0

Kudos [?]: 4 [0], given: 1

Re: inscribed circle in half circle [#permalink]  30 Aug 2010, 08:23
So, we can conclude that the question is not quite good. the composer of the test should review and make some adjustments.
Manager
Joined: 07 Oct 2006
Posts: 73
Location: India
Followers: 1

Kudos [?]: 8 [0], given: 3

Re: inscribed circle in half circle [#permalink]  30 Aug 2010, 08:31
I think so... anyone having other thoughts?
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Manager
Joined: 16 Mar 2010
Posts: 190
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Kudos [?]: 65 [0], given: 9

Re: inscribed circle in half circle [#permalink]  31 Aug 2010, 02:25
I think here we have to assume that it is inscribed from the center of the half circle. However gmat will give this statement.
Re: inscribed circle in half circle   [#permalink] 31 Aug 2010, 02:25
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