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mirhaque
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If a circle circumscribed about an equilateral triangle with side a, what is the diameter of the circle in terms of a?

please explain your answer. Thanks



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ps: circle & equilate triangle 11 Jun 2005, 10:06
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mirhaque
If a circle circumscribed about an equilateral triangle with side a, what is the diameter of the circle in terms of a?

please explain your answer. Thanks
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The diameter = 2*(2/3)*(sqrt(3)/2)*a
=(twice)(radius)
=(twice)(2/3)median
=(twice)(2/3)(sqrt(3)/2)(side)
=2*(2/3)*(sqrt(3)/2)*a

HMTG.
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It is the circum centre of the triangle . So it is 2/3a
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I have posted as (2/3) *a that is the radius...So the diameter is (4/3)*a
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mirhaque
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gmat2me2
I have posted as (2/3) *a that is the radius...So the diameter is (4/3)*a
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I am not fimiliar with this. can somebody pls explain the logic? Thanks
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Geez. This jooged my memory of trigonometry.

Circumradius of an equilateral triangle of side a is a/sqrt(3)

Diameter is 2a/sqrt(3)

Does anyone remember the sine rule? :wink:
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AJB77
Geez. This jooged my memory of trigonometry.

Circumradius of an equilateral triangle of side a is a/sqrt(3)

Diameter is 2a/sqrt(3)

Does anyone remember the sine rule? :wink:
Show more


is this exercise a GMAT one ?

IS trigonometry tested on gmat ?
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gmat2me2
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mirhaque
gmat2me2
I have posted as (2/3) *a that is the radius...So the diameter is (4/3)*a

I am not fimiliar with this. can somebody pls explain the logic? Thanks
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If a circle circumscribes a triangle the radius is called circum radius.

Since it is a eq. triangle the height of any eq triangle with side "a" is
(sqrt(3)/2)*a.

The circumcenter is the point of convergence of of the perpendicular bisectors of a triangle. It is 2/3 * height of a eq traingle.

Also the area of a triangle is abc/4*R where a,b,c are sides and R is the circum radius.
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mandy
is this exercise a GMAT one ?
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I think its possible.

Quote:
IS trigonometry tested on gmat ?
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Nope. But remembering some basics there might help.
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The answer is 2a/sqrt(3), or 2 sqrt(3) a / 3.

no need to memorize anything, just equate 1/3 of the entire triangle in terms of a:

(1/3) (1/2) * a * sqrt( a^2- (a/2)^2 )

to the area of a triangle with 2 sides of r and the other side of a:

(1/2) * a * sqrt( r^2 - (a/2) ^ 2)

this way you will get:

r = a / sqrt(3)

That said, I don't think I would have the time for this at the GMAT test though, took me a good 5 minutes, probably because I hadn't done math like this since middle school. :D



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