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What is Max. area of Triangle that is inscribed in Circle of

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What is Max. area of Triangle that is inscribed in Circle of [#permalink]

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New post 24 Oct 2008, 20:26
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

What is Max. area of Triangle that is inscribed in Circle of radius 5?

* I think que. ask for Equl triangle area

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Re: Triangle Area [#permalink]

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New post 24 Oct 2008, 21:37
vishalgc wrote:
What is Max. area of Triangle that is inscribed in Circle of radius 5?

* I think que. ask for Equl triangle area

Thanks


Please post the options as well.

Is the maximum area = 10*5/2 = 25 square units? I am not sure.
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Re: Triangle Area [#permalink]

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New post 24 Oct 2008, 23:26
vishalgc wrote:
What is Max. area of Triangle that is inscribed in Circle of radius 5?

* I think que. ask for Equl triangle area

Thanks


I too think that equilateral triangle inscribed in circle should have max area.

the side a of equilateral triangle = sqrt(3) * r = 5 * sqrt(3)

and area of equilateral triangle is = a^2 * sqrt(3) /4 = 25 * 3 * sqrt(3) /4

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Re: Triangle Area [#permalink]

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New post 24 Oct 2008, 23:45
alpha_plus_gamma wrote:

the side a of equilateral triangle = sqrt(3) * r



*slams his hand on his head*

isn't this a rule ??
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Re: Triangle Area [#permalink]

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New post 25 Oct 2008, 04:55
vishalgc wrote:
What is Max. area of Triangle that is inscribed in Circle of radius 5?

* I think que. ask for Equl triangle area

Thanks



What I have learnt here is that max area of such triangle will be when the triangle is right angled at the center. Hence, area = 1/2 * 5 * 5 = 12.5

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Re: Triangle Area [#permalink]

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New post 25 Oct 2008, 10:22
scthakur wrote:
vishalgc wrote:
What is Max. area of Triangle that is inscribed in Circle of radius 5?

* I think que. ask for Equl triangle area

Thanks



What I have learnt here is that max area of such triangle will be when the triangle is right angled at the center. Hence, area = 1/2 * 5 * 5 = 12.5


How can this be? A right angle triangle with right angle at center only covers a part of 1/4th of the circle. I am sure there are other ways of inscribing triangles and whose area is greater than the right angle triangle with right angle at center.

I am wondering how the side of an equilateral triangle inscribed in a circle can be derived as sqrt (3) X radius.

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Re: Triangle Area [#permalink]

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New post 25 Oct 2008, 10:51
icandy wrote:
scthakur wrote:
vishalgc wrote:
What is Max. area of Triangle that is inscribed in Circle of radius 5?

* I think que. ask for Equl triangle area

Thanks



What I have learnt here is that max area of such triangle will be when the triangle is right angled at the center. Hence, area = 1/2 * 5 * 5 = 12.5


How can this be? A right angle triangle with right angle at center only covers a part of 1/4th of the circle. I am sure there are other ways of inscribing triangles and whose area is greater than the right angle triangle with right angle at center.

I am wondering how the side of an equilateral triangle inscribed in a circle can be derived as sqrt (3) X radius.


I do not know the derivation part.

but check out the properties section here (third one)

http://en.wikipedia.org/wiki/Equilateral_triangle
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Re: Triangle Area [#permalink]

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New post 26 Oct 2008, 23:28
icandy wrote:
How can this be? A right angle triangle with right angle at center only covers a part of 1/4th of the circle. I am sure there are other ways of inscribing triangles and whose area is greater than the right angle triangle with right angle at center.

I am wondering how the side of an equilateral triangle inscribed in a circle can be derived as sqrt (3) X radius.


Thanks icandy for pointing out my silly mistake :oops:. I did not read the question properly.

Regarding side of an equilateral triangle, the side will make 120 degree angle at the center. If you drop a perpendicular line from the center to the side, this perpendicular line, the radius and half of the side will create a 30-60-90 triangle. Hence, if radius is r, half of the side will be (r/2)* sqrt(3) and the side will be 2*(r/2)*sqrt(3).

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Re: Triangle Area   [#permalink] 26 Oct 2008, 23:28
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What is Max. area of Triangle that is inscribed in Circle of

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