maratikus wrote:
How about this problem: A, B, C lie on a circle of radius 1, what is the length of BC.
1. \(AB^2 = BC^2 + AC^2\)
2. \(\angle CAB\) equals 30 degrees
It is nowhere indicated in question that it is a right angle triangle or one of the sides of triangle is diameter.
maratikus wrote:
The answer is B. Why?
State 1: From the first statement we just come to know that line AB = diameter of the circle. But we still don't know anything about line BC. It is not possible to find the length of this line using given information. So insufficient.
State 2: We just know that the angle opposite to line BC = 30. But we do not have any additional information to find the length of line BC. So insufficient.
Together we can derive that the \(\angle ACB\) equals 90 degrees, and \(\angle CAB\) equals 30 degrees.
So we can derive that \(BC = AB/2\).
Answer is C.
Answer could have been B, if the question were like this: A, B, C lie on a circle of radius 1, where points A and B are two ends of the diameter. What is the length of BC?
Please correct me if I am wrong, or missing something.
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