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Geometry - triangle in a circle

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by Brent@GMATPrepNow » Thu Jan 29, 2009 2:24 pm
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Please note that this is not an official GMAT question; it’s my attempt to create difficult (650+ level) GMAT-style questions for this forum.
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by gmatguy16 » Thu Jan 29, 2009 4:24 pm
i would say C
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by gmatguy16 » Thu Jan 29, 2009 4:53 pm
i would say C
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by Brent@GMATPrepNow » Thu Jan 29, 2009 5:32 pm
Righto.

(1) INSUFF – No idea about the length of BC

(2) INSUFF – No idea about the other sides

(1) and (2) – If the radius=6 and BC=12, then BC is the diameter. If B is the diameter, then angle BAC is 90 degrees.
We can let x=AC=AB and create the equation x^2 + x^2 = 12^2
We could solve this for x and, subsequently, find the area of the triangle.
SUFF
Answer: C
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by aroon7 » Sat Jan 31, 2009 8:39 am
Brent Hanneson wrote:Righto.

(1) INSUFF – No idea about the length of BC

(2) INSUFF – No idea about the other sides

(1) and (2) – If the radius=6 and BC=12, then BC is the diameter. If B is the diameter, then angle BAC is 90 degrees.
We can let x=AC=AB and create the equation x^2 + x^2 = 12^2
We could solve this for x and, subsequently, find the area of the triangle.
SUFF
Answer: C
Bern,

i have a question here.
is it possible to draw a right traingle such that diameter is not one of the sides of the triangle??
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by Brent@GMATPrepNow » Sat Jan 31, 2009 3:46 pm
is it possible to draw a right traingle such that diameter is not one of the sides of the triangle??
If you're referring to triangles in circles in general, the anwer is no.

See:
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by aroon7 » Sat Jan 31, 2009 4:20 pm
Brent Hanneson wrote:
is it possible to draw a right traingle such that diameter is not one of the sides of the triangle??
If you're referring to triangles in circles in general, the anwer is no.

See:
Image
Then, why is A insufficient for this problem...
if the angle subtended by the chord is 90, then that chord is the diameter.
since we have radius in the question we have all required info to solve this problem...
am i missing something?
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by Brent@GMATPrepNow » Sat Jan 31, 2009 4:26 pm
aroon7 wrote:
Brent Hanneson wrote:
is it possible to draw a right traingle such that diameter is not one of the sides of the triangle??
If you're referring to triangles in circles in general, the anwer is no.

See:
Image
Then, why is A insufficient for this problem...
if the angle subtended by the chord is 90, then that chord is the diameter.
since we have radius in the question we have all required info to solve this problem...
am i missing something?
Statement (1) provides no indication that there is a 90 degree angle in the triangle.
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by aroon7 » Sat Jan 31, 2009 4:28 pm
Brent Hanneson wrote:
aroon7 wrote:
Brent Hanneson wrote:
is it possible to draw a right traingle such that diameter is not one of the sides of the triangle??
If you're referring to triangles in circles in general, the anwer is no.

See:
Image
Then, why is A insufficient for this problem...
if the angle subtended by the chord is 90, then that chord is the diameter.
since we have radius in the question we have all required info to solve this problem...
am i missing something?
Statement (1) provides no indication that there is a 90 degree angle in the triangle.
i was fooled by the diagram...
:oops:
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by vikram_k51 » Sun Feb 01, 2009 4:37 am
1:AC=AB

Not Sufficient.We don't know whether,BC is the diameter.It can be a simple chord as well.

2.BC=12;

Implies ABC is a right angled trianlge.

Area of a right triangle=1/2*a*b(AC=a;AB=b;)

We know:a^2+b^2=144.But this is not sufficient.

Together with A,the soln is Sufficient.

Hence C
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