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Diameter of circle

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by samirpandeyit62 » Wed Oct 03, 2007 12:01 am
perimeter of the triangle = 24

so side =8

area = 1/2 * b *h = 1/2 *8 * 4sqrt3 = 16sqrt3

also area = product of sides/2D (where D is the diameter of circle)

= 8 ^3 /2D

so 16sqrt3 = 8^3/2D

D = 16/sqrt3

= 9 approx
Regards
Samir
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by shri_ankur » Wed Oct 03, 2007 12:39 am
Thanks Samir for the explanation but ans is 11 (C)
It might be 16/sqrt 2 (Just guessing :D)
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Re: Diameter of circle

by ratindasgupta » Wed Oct 03, 2007 6:44 am
shri_ankur wrote:An equilateral triangle is inscribed on a circle.
Perimeter of triangle is 24 cm.
What is the diameter of the circle?

a) 9 cm
b) 10 cm
c) 11 cm
d) 12 cm
e) 13 cm
Samir is right. The answer is approx 9cm.

The way ive worked it out is the height of the triangle is
√3/2*(side) = 4√3

since radius of circle is 2/3 of height, the diameter is 4/3 of height.

Therefore 4/3*4√3 = 16/√3 = approx 9
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by camitava » Wed Oct 03, 2007 6:55 am
Samir, I have a question! According to ur explanation -
perimeter of the triangle = 24

so side =8

area = 1/2 * b *h = 1/2 *8 * 4sqrt3 = 16sqrt3

also area = product of sides/2D (where D is the diameter of circle)
Is the bold lettered statement a hypothesis? I am asking because obviously I don;t know abt that. Can u pls elaborate it little more?
Correct me If I am wrong


Regards,

Amitava
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by shri_ankur » Wed Oct 03, 2007 6:59 am
Yes 9 is the correct Ans.
Thanks a lot for the explanation.
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by samirpandeyit62 » Wed Oct 03, 2007 7:12 am
Hi All,
Well Amitava

The area of a triangle(any triangle i.e equilateral, isoceles etc) inscribed within a circle is given by the formula

A = a*b*c/4R

(u are free to browse the net if u have doubts on this one, just make sure ur keywords are "Area of a triangle inscribed in a Circle")

where a,b,c are sides of the triangle & R is the circumradius i.e radius of the circle inscribing it.

I only replaced 4R by 2D

hope this is clear.
Regards
Samir
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by ratindasgupta » Wed Oct 03, 2007 9:59 am
Ok first of all, you're approach is right but one assumption is wrong. A 3-4-5 sided right angled triangle cannot be a 30-60-90 triangle.

If the side opposite 60 degree is 4, then the side opposite 30 must be 4/√3 and the hypotenuse must be 8/√3. So if the radius is 8/√3, the diameter will be 16/√3, which is approx 9.

Hope this clears your doubt.
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by gabriel » Wed Oct 03, 2007 10:59 am
the radius of a circle circumscribing a equilateral triangle is given by a/root(3) , where a is the side of the equilateral triangle ..
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by wongee » Wed Oct 03, 2007 5:50 pm
Gabriel,

Is this a known formula and does it work universally? Or it is more a conclusion.

thanks.
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by camitava » Wed Oct 03, 2007 8:11 pm
Wongee! U said -
Is this a known formula and does it work universally? Or it is more a conclusion.
Nop it is not a conclusion but a known formula. I have checked it in net. AND above all, thanks to everyone (involved in this discussion) - specially Ratin, Samir and Gabriel - for clearifying my doubts. I really did not know this fact/ theorem/ hypothesis before! :oops: :D :wink:
Correct me If I am wrong


Regards,

Amitava
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by gabriel » Wed Oct 03, 2007 10:41 pm
wongee wrote:Gabriel,

Is this a known formula and does it work universally? Or it is more a conclusion.

thanks.
well, i dont know wether this is known or not ( apparently it is not that well known, coz u wouldnt be asking this question in the first place if it was well known :wink: ) , but it is a formula that helps fasten things up when u have such questions ... btw this works only for equilateral triangles..
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by wongee » Thu Oct 04, 2007 11:17 am
Thanks Gabriel,

Well it coudl be known, and I could be the ignorant one! :-) But, i realize that this can work with an Eq tri only.
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