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In the figure shown, triangle ABC is inscribed in the circle. What is

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In the figure shown, triangle ABC is inscribed in the circle. What is  [#permalink]

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New post Updated on: 02 Sep 2015, 03:22
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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.

Attachment:
geometry.png
geometry.png [ 5.88 KiB | Viewed 13775 times ]

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Originally posted by shakticnb on 02 Sep 2015, 02:59.
Last edited by Bunuel on 02 Sep 2015, 03:22, edited 1 time in total.
Edited the question.
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Re: In the figure shown, triangle ABC is inscribed in the circle. What is  [#permalink]

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New post 02 Sep 2015, 03:37
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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
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Re: In the figure shown, triangle ABC is inscribed in the circle. What is  [#permalink]

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New post 21 Sep 2015, 12:43
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shakticnb wrote:
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.

Attachment:
geometry.png


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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In the figure shown, triangle ABC is inscribed in the circle. What is  [#permalink]

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New post 03 Sep 2015, 03:37
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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.

The answer is E.
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In the figure shown, triangle ABC is inscribed in the circle. What is  [#permalink]

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New post 26 Sep 2016, 14:50
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

Answer E
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Re: In the figure shown, triangle ABC is inscribed in the circle. What is  [#permalink]

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New post 27 Sep 2016, 06:06
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when ratios are given, 3:4:5 it implies that the values can be 3,4,5 or 6,8,10 etc

for each value, there will be different diameter value

So E
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Re: In the figure shown, triangle ABC is inscribed in the circle. What is  [#permalink]

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New post 12 Jul 2017, 09:51
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E is likely the answer.

Using 1) & 2) together, if the AB is the diameter C is 90 degrees,

:arrow: 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.

The answer is E.
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Re: In the figure shown, triangle ABC is inscribed in the circle. What is  [#permalink]

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