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Points A, B, and C lie on a circle of radius. What is the

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Points A, B, and C lie on a circle of radius. What is the [#permalink] New post 19 Nov 2007, 05:42
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C
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E

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Points A, B, and C lie on a circle of radius 1. What is the area of triangle ABC?

(1) ab^2= bc^2 + ac^2
(2) angle CAB equals 30 degrees

This question is discussed here: if-points-a-b-and-c-lie-on-a-circle-of-radius-1-what-is-84423.html and here if-points-a-b-and-c-lie-on-a-circle-of-radius-1-what-is-111134.html

Last edited by Bunuel on 17 Jul 2012, 02:21, edited 2 times in total.
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 [#permalink] New post 19 Nov 2007, 07:18
To my mind, from the data given we can only say what is the area of this triangle in terms of R (radius), but we won't be able to get a number in the answer. So my answer is E. Is it right?
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Re: Points A, B, and C lie on a circle of radius. What is the [#permalink] New post 16 Jul 2012, 15:56
My answer is (E)

1) statement 1 tells us the triangle MUST BE a RIGHT TRIANGLE because it follows the equations ab^2= bc^2 + ac^2 , with ab as the hypotunuse of the circle. Because we know the triangle is a right triangle, inscribed in a circle, then the hyptonuse, ab, MUST BE the diameter. But this doesn't tell us anything about the length of the the sides. Hence, insufficient.

2) Tells us that one of the angles is 30 degrees . Thats not much of help, because its not necessary that any of the sides be the diameter and therefore, we cannot derive any information about the radius. Not to mention, even if we had known one of the sides as the diamter, an therefore a right triangle, making a 30-60-90 triangle, we know the proporations of the angles nothing about the length of the sides. This is not sufficient.

(1) & (2) We know the triangle is a right triangle and of the sides is a 30*. But we don't anything about the sides. Hence, insufficient.

Can someone double check my work. Thank you!
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Re: Points A, B, and C lie on a circle of radius. What is the [#permalink] New post 16 Jul 2012, 16:38
Answer is E.

We dont have enough information to find the area.
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Re: Points A, B, and C lie on a circle of radius. What is the [#permalink] New post 16 Jul 2012, 18:09
ab is not line ab, but the multiplication of two sides a and b

a= BC, b = AC and c=AB. The smaller a b c are basically the lines opposite angle A B and C respectively.

I suppose radius is given, if so

Then statement 2 is sufficient. As we know angle and radius. This would give us the adjoining sides and area = 1/2 bc SinA.

Statement 1: I m short of time and will update this later. But looking at the equation most likely not sufficient.
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Re: Points A, B, and C lie on a circle of radius. What is the [#permalink] New post 17 Jul 2012, 02:21
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Re: Points A, B, and C lie on a circle of radius. What is the   [#permalink] 17 Jul 2012, 02:21
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