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adam15 · Fri Nov 20, 2009 5:25 pm

For the triangle shown above, where A, B and C are all points on a circle, and line segment AB has length 18, what is the area of triangle ABC?

(1) Angle ABC measures 30°.

(2) The circumference of the circle is 18.

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sunnyjohn · Fri Nov 20, 2009 7:41 pm

I think there is some problem with ur statement B,
as the maximum lenght of chord in a circle is diameter.
then circumference of circle if 18, then diameter should = 18/3.14 ==> in this case how can chord in the circle is 18.

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adam15 · Fri Nov 20, 2009 10:44 pm

in this DS I chose A, but I was wrong, I will post the answer after discusion

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palvarez · Sat Nov 21, 2009 2:18 am

1. angle ABC = 30; therefore, arc AC = 60 degrees. From this, we can conclude AC = radius
Computing the area of triangle requires: 2 sides, and the angle between those two sides. Insufficient

2. Circumference = 18. Diameter = 18/(3.14) < 6

A bad question written by wannabes!

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sunaina jain · Sat Nov 21, 2009 8:59 pm

IMO answer is E.

Since to measure the area one needs base and height. There is no data we can get from 1 and 2.

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brick2009 · Sat Nov 21, 2009 9:48 pm

I have a question....

Can we assume AB is the diameter..??? (since none of GMAT drawings are to scale...can we assume AB is the diameter..)

My calc. is based on AB = diameter

a.) Any triangle with diameter as the base , the angle opposite to the diameter is always 90.

hence we can solve...to get the area.

b.) B --> is no use..

A is the answer....

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adam15 · Sat Nov 21, 2009 10:03 pm

that is the trick, in the solution AB is not the diameter, choice 2 proves that AB is the diameter, and then you can solve the problem and the right answer was "C", and I was astonished

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adam15 · Sat Nov 21, 2009 10:07 pm

this is the answer for the problem

"In order to find the area of the triangle, we need to find the lengths of a base and its associated height. Our strategy will be to prove that ABC is a right triangle, so that CB will be the base and AC will be its associated height.

(1) INSUFFICIENT: We now know one of the angles of triangle ABC, but this does not provide sufficient information to solve for the missing side lengths.

(2) INSUFFICIENT: Statement (2) says that the circumference of the circle is 18. Since the circumference of a circle equals times the diameter, the diameter of the circle is 18. Therefore AB is a diameter. However, point C is still free to "slide" around the circumference of the circle giving different areas for the triangle, so this is still insufficient to solve for the area of the triangle.

(1) AND (2) SUFFICIENT: Note that inscribed triangles with one side on the diameter of the circle must be right triangles. Because the length of the diameter indicated by Statement (2) indicates that segment AB equals the diameter, triangle ABC must be a right triangle. Now, given Statement (1) we recognize that this is a 30-60-90 degree triangle. Such triangles always have side length ratios of

1::2

Given a hypotenuse of 18, the other two segments AC and CB must equal 9 and 9 respectively. This gives us the base and height lengths needed to calculate the area of the triangle, so this is sufficient to solve the problem.

The correct answer is C."
Manhatan

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