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Analytical Geometry

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Joined: 26 Nov 2008
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5 Jan 2009 11:21:43 IST
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a question of circle
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Analytical Geometry

find area of equilateral triangle inscribed in the circle


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Prakhar Banga 's Avatar

Prakhar Banga
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Joined: 20 Dec 2008
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6 Jan 2009 09:02:34 IST
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Let the triangle be ABC and the centre of the circle be O.

Therefore, angle AOB = 120 degrees and angle ABO = 30 degrees.

So By sine rule


AO is the radius. Let it be r. AB is the side of the triangle. Let it be a.


So a = r.



That means the radius of the circle is


The side a is therefore .


The area of the triangle is =

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Sagar Saxena's Avatar

Sagar Saxena
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7 Jan 2009 00:03:14 IST
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hello dear..


the radius of the circle with given equation is :


r        =            (g2  +  f2  -  c)1/2


for equitlateral traingle


r = a / root(3)


area of traingle = root(3) /  4  *  a2


now solve it ,you will get the answwer


 
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Sagar Saxena's Avatar

Sagar Saxena
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7 Jan 2009 00:04:04 IST
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cheers.............
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