Area of Triangle inside a Circle

[DarkKnight]

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.

[Anurag@Gurome]

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

Statement 1: Implies ABC is a right-angled triangle with angle ACB = 90 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.

[Night reader]

this is Manhattan GMAT question and I disagree about C, please see the following posts https://gmatclub.com/forum/area-of-trian ... ml#p895310

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.

[DarkKnight]

@Nightreader, the source that I am using states that OA for this question is C.

[Night reader]

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.

[gmatmachoman]

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.

Plz dont be so hasty..else u may not share ur 760 doc to me NR!!