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# What is the greatest possible area of a triangular region wi

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Founder
Joined: 18 Apr 2015
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What is the greatest possible area of a triangular region wi [#permalink]  25 Jul 2020, 09:45
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Question Stats:

87% (00:34) correct 12% (03:01) wrong based on 8 sessions
What is the greatest possible area of a triangular region with one side that corresponds with the diameter of a circle with radius 6, and the other vertex of the triangle on the circle?

(A) 24
(B) 36
(C) 40
(D) 48
(E) 72
[Reveal] Spoiler: OA

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Intern
Joined: 25 Jul 2020
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Re: What is the greatest possible area of a triangular region wi [#permalink]  25 Jul 2020, 11:06
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See the attached image. The key is to place the vertex in such a way that dropping a perpendicular from it will go through the center of the circle. Area is base * height = 36.
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gre123.png [ 7.43 KiB | Viewed 151 times ]

Manager
Joined: 02 May 2020
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Re: What is the greatest possible area of a triangular region wi [#permalink]  26 Jul 2020, 09:13
1
KUDOS
Since the base will be same for all such triangles but height will vary, the triangle with maximum area will be the one where the perpendicular dropped from the third vertex on the side coinciding with the diameter passes through the center (the yellow triangle present in the figure).

So,
Max area = (1/2)*(12)*(6) = 36

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answer.png [ 11.49 KiB | Viewed 116 times ]

Re: What is the greatest possible area of a triangular region wi   [#permalink] 26 Jul 2020, 09:13
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