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# One of the sides of a triangle tht inscribe in a circle is 6

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One of the sides of a triangle tht inscribe in a circle is 6  [#permalink]

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25 Jun 2013, 02:08
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68% (01:26) correct 32% (01:37) wrong based on 214 sessions

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One of the sides of a triangle that inscribe in a circle is 6. Is the triangle a right triangle?

(1) Two of the sides of the triangle have the same length.
(2) The circumference of the circle is 6 pi.

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Re: One of the sides of a triangle tht inscribe in a circle is 6  [#permalink]

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25 Jun 2013, 02:21
One of the sides of a triangle that inscribe in a circle is 6. Is the triangle a right triangle?

(1) Two of the sides of the triangle have the same length. Know nothing about the circle. Not sufficient.

(2) The circumference of the circle is 6 pi --> $$2\pi{r}=6\pi$$ --> $$r=3$$ --> $$diameter=6$$. So, one of the sides of the triangle is the diameter of the circle. Now, a right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle. Sufficient.

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Re: One of the sides of a triangle tht inscribe in a circle is 6  [#permalink]

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25 Jun 2013, 02:55
Bunuel wrote:
One of the sides of a triangle that inscribe in a circle is 6. Is the triangle a right triangle?

(1) Two of the sides of the triangle have the same length. Know nothing about the circle. Not sufficient.

(2) The circumference of the circle is 6 pi --> $$2\pi{r}=6\pi$$ --> $$r=3$$ --> $$diameter=6$$. So, one of the sides of the triangle is the diameter of the circle. Now, a right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle. Sufficient.

yeah .. exactly .. When I posted this question I was inscribing circle in the triangle .. when I went back to it, I realized this is fairly easy question.
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Re: One of the sides of a triangle tht inscribe in a circle is 6  [#permalink]

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05 Nov 2013, 21:59
Bunuel wrote:
One of the sides of a triangle that inscribe in a circle is 6. Is the triangle a right triangle?

(1) Two of the sides of the triangle have the same length. Know nothing about the circle. Not sufficient.

(2) The circumference of the circle is 6 pi --> $$2\pi{r}=6\pi$$ --> $$r=3$$ --> $$diameter=6$$. So, one of the sides of the triangle is the diameter of the circle. Now, a right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle. Sufficient.

Hi,

I am not clear on the answer B. If a triangle is inscribed in the circle then it is definitely right angle. However, shouldnt we consider the option where two other sides are not in the circle and the triangle then formed could be an equilateral triangle or a scalene triangle - in which case the triangle is not a right angle. Please advise. thanks, Amita
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Re: One of the sides of a triangle tht inscribe in a circle is 6  [#permalink]

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06 Nov 2013, 03:14
1
amitasagar23 wrote:
Bunuel wrote:
One of the sides of a triangle that inscribe in a circle is 6. Is the triangle a right triangle?

(1) Two of the sides of the triangle have the same length. Know nothing about the circle. Not sufficient.

(2) The circumference of the circle is 6 pi --> $$2\pi{r}=6\pi$$ --> $$r=3$$ --> $$diameter=6$$. So, one of the sides of the triangle is the diameter of the circle. Now, a right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle. Sufficient.

Hi,

I am not clear on the answer B. If a triangle is inscribed in the circle then it is definitely right angle. However, shouldnt we consider the option where two other sides are not in the circle and the triangle then formed could be an equilateral triangle or a scalene triangle - in which case the triangle is not a right angle. Please advise. thanks, Amita

That's not correct. Any triangle can be inscribed in a circle: scalene, obtuse, right.

Also, inscribed triangle means that the vertices of the triangle are on the circle.
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Re: One of the sides of a triangle tht inscribe in a circle is 6  [#permalink]

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05 Jul 2018, 06:51
Bunuel wrote:
One of the sides of a triangle that inscribe in a circle is 6. Is the triangle a right triangle?

(1) Two of the sides of the triangle have the same length. Know nothing about the circle. Not sufficient.

(2) The circumference of the circle is 6 pi --> $$2\pi{r}=6\pi$$ --> $$r=3$$ --> $$diameter=6$$. So, one of the sides of the triangle is the diameter of the circle. Now, a right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle. Sufficient.

Hello Bunuel,
Why can't we conclude from the first statement that the triangle is not a right angle since it is said to be an isosceles triangle? Since the triangle is inscribed in a circle, I think the only way for a triangle to be isosceles is when the two sides of the triangle are the radii of the circle. Please inform me where my understanding might be wrong.
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Re: One of the sides of a triangle tht inscribe in a circle is 6  [#permalink]

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05 Jul 2018, 07:35
MrJglass wrote:
Bunuel wrote:
One of the sides of a triangle that inscribe in a circle is 6. Is the triangle a right triangle?

(1) Two of the sides of the triangle have the same length. Know nothing about the circle. Not sufficient.

(2) The circumference of the circle is 6 pi --> $$2\pi{r}=6\pi$$ --> $$r=3$$ --> $$diameter=6$$. So, one of the sides of the triangle is the diameter of the circle. Now, a right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle. Sufficient.

Hello Bunuel,
Why can't we conclude from the first statement that the triangle is not a right angle since it is said to be an isosceles triangle? Since the triangle is inscribed in a circle, I think the only way for a triangle to be isosceles is when the two sides of the triangle are the radii of the circle. Please inform me where my understanding might be wrong.

Check the image below:

Attachment:

Untitled.png [ 20.15 KiB | Viewed 651 times ]

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Re: One of the sides of a triangle tht inscribe in a circle is 6  [#permalink]

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05 Jul 2018, 09:51
Bunuel wrote:
MrJglass wrote:
Bunuel wrote:
One of the sides of a triangle that inscribe in a circle is 6. Is the triangle a right triangle?

(1) Two of the sides of the triangle have the same length. Know nothing about the circle. Not sufficient.

(2) The circumference of the circle is 6 pi --> $$2\pi{r}=6\pi$$ --> $$r=3$$ --> $$diameter=6$$. So, one of the sides of the triangle is the diameter of the circle. Now, a right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle. Sufficient.

Hello Bunuel,
Why can't we conclude from the first statement that the triangle is not a right angle since it is said to be an isosceles triangle? Since the triangle is inscribed in a circle, I think the only way for a triangle to be isosceles is when the two sides of the triangle are the radii of the circle. Please inform me where my understanding might be wrong.

Check the image below:

Attachment:
Untitled.png

Okay! Thanks!

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Re: One of the sides of a triangle tht inscribe in a circle is 6 &nbs [#permalink] 05 Jul 2018, 09:51
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