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Analytical Geometry

New kid on the Block

 Joined: 26 Nov 2008 Post: 18
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

Blazing goIITian

Joined: 20 Dec 2008
Posts: 599
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 =

Blazing goIITian

Joined: 8 Oct 2008
Posts: 8064
7 Jan 2009 00:03:14 IST
1 people liked this

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

Blazing goIITian

Joined: 8 Oct 2008
Posts: 8064
7 Jan 2009 00:04:04 IST
0 people liked this

cheers.............

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