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Rectangle inscribed in a circle

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Rectangle inscribed in a circle

by psm12se » Wed Jan 01, 2014 7:36 am

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If a rectangle is inscribed in a circle of radius 5, is the area of the rectangle greater than 48

A. The ratio of the lengths of sides of the rectangle is 3:4

B. The difference between the lengths of sides of the rectangle is smaller than 3
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Source: — Data Sufficiency |
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by Uva@90 » Wed Jan 01, 2014 10:01 pm

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psm12se wrote:If a rectangle is inscribed in a circle of radius 5, is the area of the rectangle greater than 48

A. The ratio of the lengths of sides of the rectangle is 3:4

B. The difference between the lengths of sides of the rectangle is smaller than 3
Hi Psm12se,

Here are few thing to note,
1) any Side of a rectangle can't be more than 10. since diameter is 10.
2) Side need not only be integers.
3) Diagonal of an inscribed rectangle is always the diameter of a circle.

To Find: IS Area > 48 (Yes/No Type)

Statement 1: l/b =The ratio of the lengths of sides of the rectangle is 3:4
so sides should be 6 and 8 (6^2+8^2 =100)
6*8 =48 !>48
Hence Sufficient.

Statement 2: The difference between the lengths of sides of the rectangle is smaller than 3

sides can be 6 and 8 (6^2+8^2 =100) 8-6 =2 <3 6*8 =48 =NO
Side can be 5sqrt(2) 5sqrt(2) (50+50=100): 0<3 50 >48 Yes
Hence In-sufficient.

Hence Answer is A

Regards,
Uva.
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by psm12se » Wed Jan 01, 2014 11:10 pm

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Thanks for the reply.

OA is A but I choose answer as E because in this question, it is not stated explicitly that the vertices of the rectangle are on the circle.
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by ceilidh.erickson » Mon Jan 06, 2014 5:01 pm

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psm12se wrote:OA is A but I choose answer as E because in this question, it is not stated explicitly that the vertices of the rectangle are on the circle.

I understand your concern, and it's good that you're thinking about alternative possible shapes. However, whenever the GMAT uses the word "inscribed" in a geometry question, it means that the vertices of one figure touch the sides of the other figure. A rectangle inscribed in a circle must have all of its vertices touching the circle.
Ceilidh Erickson
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by aashishagarwal » Thu Aug 31, 2017 3:52 am

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Why the answers are hidden?
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by [email protected] » Thu Aug 31, 2017 10:13 am

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Hi aashishagarwal,

As a 'courtesy' to people who are attempting this question, most other posters hide the correct answer choice from view (although if you scroll over the 'blacked-out' portion, you will be able to see the correct answer). This is so you don't 'accidentally' see the correct answer while you're reading through the prompt (or working on it).

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