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Gmat Prep - Circle/Triangle

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Senior | Next Rank: 100 Posts
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by lux » Sun May 04, 2008 3:23 pm
QUESTION: What is the greatest possible area of a triangular region with one vertex at the center of a circle of radius 1 and the other two vertices on the circle?

A. square root 3/4
B. 1/2
C. pi/4
D. 1
E. square root 2

B

Please help explain thanks!
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by ksh » Sun May 04, 2008 10:36 pm
The inscribed triangle will have maximum are when it is a right angled triangle.

Therefore, area= 1/2

Is the ans correct?
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by shrikantkamble » Sun May 04, 2008 11:16 pm
Hi,

one vertex passing through Center indicates that, its a right angle triangle. One of the side of right angle triagle is fixed. ie double of radius.
ie 2.

As per area of triangle 1/2 * Height * Base.
Base = 2.

If we consider maximum height of the Triangle ie Radius, ie height = 1

Hence,
area = 1/2 * Height * Base
area = 1/2 * 2 * 1
area = 1

I think, Correct answer is D.
Thanks & Regards,
Shrikant
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