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

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Manager
Joined: 20 Jun 2012
Posts: 98
Location: United States
Concentration: Finance, Operations
GMAT 1: 710 Q51 V25
One of the sides of a triangle tht inscribe in a circle is 6 [#permalink]

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25 Jun 2013, 01:08
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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.
[Reveal] Spoiler: OA

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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, 01:21
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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. 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, 01:55
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, 20:59
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, 02:14
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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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14 Jan 2018, 05:20
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Re: One of the sides of a triangle tht inscribe in a circle is 6   [#permalink] 14 Jan 2018, 05:20
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