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What is the greatest possible area of triangular region with

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What is the greatest possible area of triangular region with [#permalink] New post 04 Apr 2007, 15:52
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What is the greatest possible area of triangular region with one vertex at the center of the a circle with 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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 [#permalink] New post 04 Apr 2007, 16:59
OA is B.

Thanks!

Nitin
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 [#permalink] New post 04 Apr 2007, 17:12
Trvikram,

How did you figure out that this would be the triangle with largest area?

thanks!
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Answer is 1/2 [#permalink] New post 04 Apr 2007, 19:26
The measure of an inscrbed angle is 1/2 of the measure of the intercepted arc. This is a theorem. An inscribed angle is an angle with its vertex on the circle and the sides of it contain chords of the circle.

The maximum inscribed angle that can be formed in this instance is 90 degrees since the maximum angle of the arc that can be formed is 180 degrees (A semi-circle). By this theorem the inscribed angle becomes 90 degrees which forms the height of the triangle. Now apply the formula 1/2 * b * h which gives us 1/2.
Answer is 1/2   [#permalink] 04 Apr 2007, 19:26
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