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What is the greatest possible area of a triangular region wi

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What is the greatest possible area of a triangular region wi [#permalink] New post 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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Re: What is the greatest possible area of a triangular region wi [#permalink] New post 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
gre123.png [ 7.43 KiB | Viewed 146 times ]

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

Answer is B.
Attachments

answer.png
answer.png [ 11.49 KiB | Viewed 111 times ]

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

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