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Geometry

by awilhelm » Thu Jan 29, 2009 8:36 pm
What is the greatest possible area of a triangular region with one vertx at the center of a circle of radius 1 and the other two vertices on the circle?

a) (sqrt3)/4
b) 1/2
c) pi/4
d) 1
e) sqrt2
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by krisraam » Thu Jan 29, 2009 8:46 pm
IMO B.

I think if one of the vertex at center and the other two on the circle. The area of any triangle formed like that will have the area 1/2 * 1 * 1 = 1/2.


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Raama
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by krisraam » Thu Jan 29, 2009 8:53 pm
Area of a isosceles triangle is maximum if the angles are 45/45.

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by awilhelm » Thu Jan 29, 2009 8:53 pm
Not exactly. Picture one vertex at the center of the circle and the other two vertices at two points on the circle one millimeter apart from each other. The area of that triangle will certainly be less than 1/2.

I'm not sure how to prove that 1/2 is the greatest possible area, though.
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by awilhelm » Thu Jan 29, 2009 8:54 pm
Ok, thanks.
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