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# Circle Inscribed in a Semicircle

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Manager
Joined: 19 Mar 2012
Posts: 171
Location: United States
Concentration: Finance, General Management
GMAT 1: 750 Q50 V42
GPA: 3.69
WE: Analyst (Mutual Funds and Brokerage)
Circle Inscribed in a Semicircle [#permalink]

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04 Apr 2012, 08:45
ajrox wrote:
Hey guys,

Excuse me if I am misunderstanding something basic, but what does inscribe mean? Does it not mean that the smaller circle is just completely inside the half-circle (touching all sides possible) (Not necessarily in the centre). So, when I read the question, I can't figure where this smaller circle is exactly.

As per my understanding, we can have infinite circles inscribed in the half-circle, touching all sides of the half-circle at various points, with of course, the biggest one in the centre.

So, why have we assumed that its centre is on the radius of the half circle?

I'm taking this post from another poster but I never saw the question answered and was wondering if someone could give an explanation. I know that a circle inscribed in a polygon has each side of the polygon tangent to the circle. But when a circle is inscribed in a semicircle, how do we know where the circle is placed. In the figure drawn by the above poster, is each circle shown considered to be "inscribed?

For more context, this question is in reference to the test question below:

Quote:
A circle is inscribed in a half circle with a diameter of π. 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
Math Expert
Joined: 02 Sep 2009
Posts: 39702
Re: Circle Inscribed in a Semicircle [#permalink]

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04 Apr 2012, 08:49
1
KUDOS
Expert's post
Swoosh617 wrote:
ajrox wrote:
Hey guys,

Excuse me if I am misunderstanding something basic, but what does inscribe mean? Does it not mean that the smaller circle is just completely inside the half-circle (touching all sides possible) (Not necessarily in the centre). So, when I read the question, I can't figure where this smaller circle is exactly.

As per my understanding, we can have infinite circles inscribed in the half-circle, touching all sides of the half-circle at various points, with of course, the biggest one in the centre.

So, why have we assumed that its centre is on the radius of the half circle?

I'm taking this post from another poster but I never saw the question answered and was wondering if someone could give an explanation. I know that a circle inscribed in a polygon has each side of the polygon tangent to the circle. But when a circle is inscribed in a semicircle, how do we know where the circle is placed. In the figure drawn by the above poster, is each circle shown considered to be "inscribed?

For more context, this question is in reference to the test question below:

Quote:
A circle is inscribed in a half circle with a diameter of π. 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

Check this: a-circle-is-inscribed-in-a-half-circle-with-a-diameter-of-127988.html
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Manager
Joined: 17 Oct 2011
Posts: 240
Location: United States
Concentration: Strategy, Marketing
GMAT 1: 720 Q51 V36
Re: Circle Inscribed in a Semicircle [#permalink]

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04 Apr 2012, 08:51
1
KUDOS
you are right and there is no reason to assume such. when you see a question like this on the actual GMAT, it will most definitely be accompanied by a figure to exclude any ambiguity.
_________________
Manager
Joined: 19 Mar 2012
Posts: 171
Location: United States
Concentration: Finance, General Management
GMAT 1: 750 Q50 V42
GPA: 3.69
WE: Analyst (Mutual Funds and Brokerage)
Re: Circle Inscribed in a Semicircle [#permalink]

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04 Apr 2012, 09:04
Thanks guys, good to know. Just wanted to make sure I wasn't missing something
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7443
Location: Pune, India
Re: Circle Inscribed in a Semicircle [#permalink]

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04 Apr 2012, 19:47
Let me add one more point here: This is a PS question so we know that we can find the answer using the given information. If such a question comes in GMAT, it will definitely be more explicit about the circle it wants you to consider. A diagram may or may not be given.
But if it were a DS question, they could give you a diagram showing just the center circle to trick you. You need to consider the other possibilities too.
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Re: Circle Inscribed in a Semicircle   [#permalink] 04 Apr 2012, 19:47
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