Geometry

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parveen110: Senior | Next Rank: 100 Posts; Posts: 91; Joined: Fri Jan 17, 2014 7:34 am; Thanked: 7 times

by parveen110 » Mon Jun 02, 2014 1:50 am

There are two concentric circles such that the area of the outer circle is four times the area of the inner circle. Let A, B, and C be three distinct points on the perimeter of the outer circle such that AB and AC are tangents to the inner circle. If the area of the triangle ABC is 9Root3/PI square centimeters, then the area of the outer circle is:

A) 9/4
B) 9/PI
C) 12
D) 12 pi
E) 12Root3

When i assume given triangle to be an equilateral then i can solve it.

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Source: Beat The GMAT — Problem Solving | Mon Jun 02, 2014 1:50 am

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Mon Jun 02, 2014 8:50 am

It will be equilateral only.

R A H U L

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Mon Jun 02, 2014 10:42 am

Hi parveen110,

What is the source of this question? I only ask because it feels a bit too "sophisticated" for a typical multi-shape geometry question on the GMAT.

Since the area of the bigger circle is 4 times the area of the smaller circle, that means the radius of the bigger circle is twice the radius of the smaller circle. This is the exact scenario that it takes to create an equilateral triangle. If the inner circle is a little bigger or a little smaller, then the triangle wouldn't be equilateral.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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prachi18oct: Master | Next Rank: 500 Posts; Posts: 269; Joined: Sun Apr 27, 2014 10:33 pmFollowed by: 5 members; Thanked: 8 times

by prachi18oct » Thu Jun 05, 2014 6:51 am

Can you please provide the solution of this one? Also how it is equilateral triangle? BC is not a straight line ..then how is it a triangle?

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Thu Jun 05, 2014 7:47 am

Rich is right - this is much harder than a standard GMAT geometry question, and the language is not exactly GMAT-like. It's fine to do challenge problems for practice, but just know that this is not a task that you'd be expected to perform on the GMAT.

Please always post the source to every question, so other students can evaluate how helpful those sources are.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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