If points A, B, and C lie on a circle of radius 1, what is the area of triangle ABC?
1. AB^2 =AC^2+BC^2
2. Angle CAB equals 30 degrees
Answer after few replies.
Thanks.
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Area of Triangle inside a Circle
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DarkKnight
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Anurag@Gurome
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Statement 1: Implies ABC is a right-angled triangle with angle ACB = 90 degreesDarkKnight wrote:If points A, B, and C lie on a circle of radius 1, what is the area of triangle ABC?
1. AB^2 =AC^2+BC^2
2. Angle CAB equals 30 degrees
Hence, the hypotenuse AB must be a diameter of the circle as it subtends a right angle on the circumference.
Therefore, AB = 2
But still the point C is not fixed, and hence the triangle can have different areas.
Not sufficient
Statement 2: There can be infinite number of triangles with different areas.
Not sufficient
1 & 2 Together: Now we know ABC is a 30-60-90 triangle with a hypotenuse of length 2. Therefore, we can determine the length of the base and height, and hence the area.
Sufficient
The correct answer is C.
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Night reader
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this is Manhattan GMAT question and I disagree about C, please see the following posts https://gmatclub.com/forum/area-of-trian ... ml#p895310
DarkKnight wrote:If points A, B, and C lie on a circle of radius 1, what is the area of triangle ABC?
1. AB^2 =AC^2+BC^2
2. Angle CAB equals 30 degrees
Answer after few replies.
Thanks.
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com
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DarkKnight
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Night reader
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yes after double checking my solution, I revealed no possibility for us to derive the area for triangle ABC with statement (2). agree about C.
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com
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gmatmachoman
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Plz dont be so hasty..else u may not share ur 760 doc to me NR!!Night reader wrote:yes after double checking my solution, I revealed no possibility for us to derive the area for triangle ABC with statement (2). agree about C.
