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# A right triangle is inscribed in a circle. The legs of the triangle

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Math Expert
Joined: 02 Sep 2009
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A right triangle is inscribed in a circle. The legs of the triangle  [#permalink]

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06 Jun 2016, 03:37
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5% (low)

Question Stats:

93% (00:38) correct 7% (01:17) wrong based on 169 sessions

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A right triangle is inscribed in a circle. The legs of the triangle have lengths 6 and 8. What is the diameter of the circle?

(A) 8
(B) $$8\pi$$
(C) $$9\sqrt 3$$
(D) 10
(E) 12

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Re: A right triangle is inscribed in a circle. The legs of the triangle  [#permalink]

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06 Jun 2016, 04:58
diameter = hypotenuse =h
h^2 = 6^2+8^2 = 36+64=100
h=10
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A right triangle is inscribed in a circle. The legs of the triangle  [#permalink]

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06 Jun 2016, 06:43
If right triangle is inscribed in a circle, its hypothenuse will always be the diameter of the circle.

If we know that 2 legs of that right triangle are 6 & 8, then we can easily find the hypothenuse (diameter of the circle) by using the Pythagorean theorem.

$$d^2 = 6^2 + 8^2 = 100$$
d = 10
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Re: A right triangle is inscribed in a circle. The legs of the triangle  [#permalink]

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13 Jun 2016, 06:41
I have a doubt here. The question says that two legs are 6 and 8. How can we be sure that 8 is not the longest side(i.e the diameter)?
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Re: A right triangle is inscribed in a circle. The legs of the triangle  [#permalink]

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13 Jun 2016, 07:05
Bunuel wrote:
A right triangle is inscribed in a circle. The legs of the triangle have lengths 6 and 8. What is the diameter of the circle?

(A) 8
(B) $$8\pi$$
(C) $$9\sqrt 3$$
(D) 10
(E) 12

Property of a right triangle inscribed in a circle is that when an angle is made from diameter of the circle, it is a right triangle. Or if a right triangle is made inscribed in a circle, its its longest side is the diameter of the circle.

Hence diameter= (6^2+8^2)^1/2= 10

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Re: A right triangle is inscribed in a circle. The legs of the triangle  [#permalink]

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13 Jun 2016, 07:13
tallyho_88 wrote:
I have a doubt here. The question says that two legs are 6 and 8. How can we be sure that 8 is not the longest side(i.e the diameter)?

Good question my friend !!

There are however two things to note.
1.The triangle is a right triangle
2.The triangle is inscribed in a circle .

and I believe inscribed means a geometrical shape which would fit (properly with all the vertices touching the circle) inside the other,
and if the shape, which is this case is a triangle fits , it must have all 3 vertices touching the circle ,also since it is a right triangle the diameter will subtend 90 degree angle on the circle.
Hence 8 cannot be the diameter.
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A right triangle is inscribed in a circle. The legs of the triangle  [#permalink]

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13 Jun 2016, 07:59
CounterSniper wrote:
tallyho_88 wrote:
I have a doubt here. The question says that two legs are 6 and 8. How can we be sure that 8 is not the longest side(i.e the diameter)?

Good question my friend !!

There are however two things to note.
1.The triangle is a right triangle
2.The triangle is inscribed in a circle .

and I believe inscribed means a geometrical shape which would fit (properly with all the vertices touching the circle) inside the other,
and if the shape, which is this case is a triangle fits , it must have all 3 vertices touching the circle ,also since it is a right triangle the diameter will subtend 90 degree angle on the circle.
Hence 8 cannot be the diameter.

oh okay...got it....i couldn't figure that out but now i guess i did... its just that if diameter is 8....radius will be 4...so it'll be difficult to fit in the triangle with all the dimensions. Thanks a lot.
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Re: A right triangle is inscribed in a circle. The legs of the triangle  [#permalink]

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15 Jun 2016, 11:55
Top Contributor
tallyho_88 wrote:
I have a doubt here. The question says that two legs are 6 and 8. How can we be sure that 8 is not the longest side(i.e the diameter)?

Good question.
In a right triangle, the longest side is called the hypotenuse, and the other two (shorter) sides (that create the right angle) are called legs.

Cheers,
Brent
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Re: A right triangle is inscribed in a circle. The legs of the triangle  [#permalink]

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17 Sep 2016, 02:21
Why doesn't the 2:1:sqr3 apply here....
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Re: A right triangle is inscribed in a circle. The legs of the triangle  [#permalink]

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12 Oct 2018, 02:45
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Re: A right triangle is inscribed in a circle. The legs of the triangle   [#permalink] 12 Oct 2018, 02:45
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