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

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

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

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

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
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Re: In the figure shown, triangle ABC is inscribed in the circle. What is [#permalink]
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vanam52923 wrote:
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

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