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## Geometry

This topic has 2 member replies
jkelk Just gettin' started!
Joined
12 Mar 2012
Posted:
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Geometry Wed Mar 14, 2012 11:50 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
Hi

Thanks,
J
[Moderator Edit: Moved the post to a relevant forum - neelgandham]
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zueswoods Rising GMAT Star
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09 Sep 2011
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Thu Mar 15, 2012 1:20 pm
Remember this:

"To maximize the area of a triangle given a base, make it a 90 degree isoceles, 90-45-45" -MGMAT book

Therefore with radius 1 (base =1), the height equals 1 and thus the area equalls 1/2.

karunamay Just gettin' started!
Joined
07 Apr 2012
Posted:
1 messages
Wed Apr 11, 2012 8:31 am
HI

In this problem it is given that one vertex of the triangle is at the center of a unit circle.
From this we conclude that if you join this vertex to other two vertex somewhere at the circle, then length of these two sides of triangle will be equal to radius of circle.
Let these sides be a, b , therefore a = b =radius of circle = 1
Let angle between these two sides is C.

Then area of the triangle =1/2*a*b* sin C

=1/2*1*1* sin C = 1/2* sin C
here we see area of the triangle solely depends on angle C.
Therefor, area of the triangle will be maximum where sin C is maximum.

Maximu value that sin function takes is 1, cosequently (sin C)max =1.

Hence, required area of the triangle = 1/2*1 =1/2.

Therefore, option B is correct.

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