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

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

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.

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

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

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

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.

is second statement enough to say that it is right angled triangle ?
as ratio is 3:4:5 which is right angled triangle.
say sides are 3x ,4x,5x
so if x is not integer will it sitll be right angled triangle?
Bunuel
chetan2u

Yes any ratio which can be simplified to 3:4:5 will be a right angled triangle..
say sides are 4.5:6:7.5 ---- it is a right angled triangle
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