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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?

Re: Points A, B, and C lie on a circle of radius. What is the [#permalink]
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.