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Re: In the figure shown, triangle ABC is inscribed in the circle. What is
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02 Sep 2015, 04:37
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Hi shakticnb,
The problem can be solved without even writing a single line. We have been asked the circumference of the circle, but none of the statements give us anything in terms of absolute values, hence we do not have sufficient information to find the answer. Option E
To dive deep:
Given: Triangle is inscribed in the Circle Required: Circumference of the circle
Statement 1: AB is the diameter of the circle. This tells us that the Circumference will be 2*pi*(AB/2) But we do not have the value of AB. INSUFFICIENT
Statement 2: This statement tells us the ratio of the sides, but nothing about the actual measurements. The sides can be 3,4,5 or 6,8,10 or 9,14,15 and so on ... INSUFFICIENT
Statements 1 and 2 combined: Still we do not have a value for any of the sides. INSUFFICIENT
Whenever diameter is one of the sides of a triangle whose 3rd vertex touch circle, then there is a right angle at third vertex. Hence, we know that it is a right angle triangle.
Also, right angle triangle has some triplets like 3 4 5 or 5 12 13 etc. It is given that we have the ratios, but not actual dimensions. So, the sides can be 3 4 5 or 6 8 10 etc. Hence there is no clear answer and E is the correct option
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Please award kudos if you like my explanation. Thanks
In the figure shown, triangle ABC is inscribed in the circle. What is
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03 Sep 2015, 04:37
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.
In the figure shown, triangle ABC is inscribed in the circle. What is the circumference of the circle?
(1) AB is a diameter of the circle. (2) The ratio of the lengths of BC, AC, and AB, respectively, is 3 : 4 : 5.
In the original condition, the triangle has 3 variables and the circle has another variable therefore there are overall 4 variables. In order to match the number of variables and equations,we need 4 equations and since there is only 1 each in 1) and 2), E is likely the answer. Using 1) & 2) together, if the AB is the diameter C is 90 degrees, and side the ratio of the length is 3:4:5, AB = 5, 10,15...thus the answer is not unique. Therefore it is not sufficient.
In the figure shown, triangle ABC is inscribed in the circle. What is
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26 Sep 2016, 15:50
Statement 1: Insuff. Since the question is asking for a value and we don't have any values given. Statement 2: Insuff since we are given ratios the sides could be any numbers in that ratio.
If we combine them we still don't have any more info
Re: In the figure shown, triangle ABC is inscribed in the circle. What is
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20 Aug 2018, 15:01
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70% (00:32) correct 
and side the ratio of the length is 3:4:5, AB = 5, 10,15...thus the answer is not unique. Therefore it is not sufficient.
