Geometry - triangle in a circle

Question

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.

gmatguy16 · Answer

i would say C

gmatguy16 · Answer

i would say C

Brent@GMATPrepNow · Answer

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

Brent Hanneson - Creator of GMATPrepNow.com

aroon7 · Answer

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??

Brent@GMATPrepNow · Answer

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:

aroon7 · Answer

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: 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?

Brent@GMATPrepNow · Answer

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: 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.

aroon7 · Answer

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: 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...

vikram_k51 · Answer

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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