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

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Bunuel
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A right triangle is inscribed in a circle. The legs of the triangle [#permalink] New post  06 Jun 2016, 04:37
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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] New post  06 Jun 2016, 05:58
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] New post  06 Jun 2016, 07:43
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
Answer: D
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Re: A right triangle is inscribed in a circle. The legs of the triangle [#permalink] New post  13 Jun 2016, 07:41
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] New post  13 Jun 2016, 08:05
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

D is the answer
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Re: A right triangle is inscribed in a circle. The legs of the triangle [#permalink] New post  13 Jun 2016, 08:13
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] New post  13 Jun 2016, 08:59
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] New post  15 Jun 2016, 12:55
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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] New post  17 Sep 2016, 03:21
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] New post  12 Oct 2018, 03:45
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Re: A right triangle is inscribed in a circle. The legs of the triangle [#permalink]
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