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What is the greatest possible area of a triangular region

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What is the greatest possible area of a triangular region [#permalink] New post 11 Oct 2008, 01:18
What is the greatest possible area of a triangular region with one vertex at the center of a circle or radius 1 and the other two
vertices on the circle?
a. sqrt 3/4
b. 1/2
c. pi/4
d. 1
e. sqrt 2
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Re: area of circle [#permalink] New post 12 Oct 2008, 21:26
How'd you come up with this answer?
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Re: area of circle [#permalink] New post 12 Oct 2008, 22:05
Area of a triangle will be maximum when it is an equlateral triangle. Hence, it should be A.
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Re: area of circle [#permalink] New post 13 Oct 2008, 01:36
isn´t it:

1= h2 + (0,5)2
0.75=h2
h= sqrt 3/4

-> Area= sqrt 3/4* / 2

can someone tell me my mistake?

cheers :-D
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Re: area of circle [#permalink] New post 13 Oct 2008, 03:35
Answer is 1/2. But i just don't know how to get to this answer
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Re: area of circle [#permalink] New post 13 Oct 2008, 04:39
A,B,C are triangle point and O is some point on circle.

See one point is on center and two are on cirle.

to have max. area we need to put this two point in such a way that distance between is max.

so line BC should cut line AO in half distance .. means you will get height =1/2 and so on..

i think its getting tough to explain it.. sorry guy
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Re: area of circle [#permalink] New post 13 Oct 2008, 12:33
Here's the explanation:
Area of a triangle : 1/2 * b * h
The area will be maximum when b = h.
Think of a triangle whose b and h is same i.e. an isosceles right angled triangle.
therefore, b = h = 1
i.e, 1/2 * 1 * 1 = 1/2
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Re: area of circle [#permalink] New post 13 Oct 2008, 12:50
nikhilpoddar wrote:
Here's the explanation:
Area of a triangle : 1/2 * b * h
The area will be maximum when b = h.
Think of a triangle whose b and h is same i.e. an isosceles right angled triangle.
therefore, b = h = 1
i.e, 1/2 * 1 * 1 = 1/2



Good catch. I did not consider that angle at the center could be the right angle.
Re: area of circle   [#permalink] 13 Oct 2008, 12:50
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