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What is the area of a triangle inscribed in a circle

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Director
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What is the area of a triangle inscribed in a circle [#permalink] New post 22 Dec 2007, 20:54
What is the area of a triangle inscribed in a circle circumscribed by a square made by joining the mid-points of the adjacent sides of a square of side 'a'.

A) 3*a^2/16

B) [3*[3^(1/2)]*a^2 ]/16

C) 3/[ 4*a^2*(Pi - (1/2))]

D) [3*[3^(1/2)]*a^2 ]/32
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CEO
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 [#permalink] New post 23 Dec 2007, 00:51
Expert's post
maybe there is a typo. Is the triangle equilateral? Otherwise, we will have a range of area instead of unique value.
B

r=a/2 - the radius of the circle.
S=1/2*a*h=1/2*(√3*r)*(3/2*r)=3*√3/4*r²=3*√3/16*a²
Director
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 [#permalink] New post 23 Dec 2007, 06:56
walker wrote:
maybe there is a typo. Is the triangle equilateral? Otherwise, we will have a range of area instead of unique value.
B

r=a/2 - the radius of the circle.
S=1/2*a*h=1/2*(√3*r)*(3/2*r)=3*√3/4*r²=3*√3/16*a²



No, there isn't any typo.

The figure, I could understand is attached. Is this the figure you also assumed?

The correct answer is "D".

Could you please explain your approach.
By the way, one more question, how do you make/type square root symbol?
Attachments

untitled.PNG
untitled.PNG [ 7.89 KiB | Viewed 641 times ]

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CEO
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 [#permalink] New post 23 Dec 2007, 09:16
Expert's post
LM wrote:
No, there isn't any typo.

The figure, I could understand is attached. Is this the figure you also assumed?

The correct answer is "D".


ahhhh......:?

LM wrote:
By the way, one more question, how do you make/type square root symbol?


I copy them form MS word or use codes:
√ - "& # 8 7 3 0 ;" (without spaces)
∞ - "& # 8 7 3 4 ;" (without spaces)
∑ - "& # 8 7 2 1 ;" (without spaces)
≠ - "& # 8 8 0 0 ;" (without spaces)
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CEO
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 [#permalink] New post 23 Dec 2007, 09:21
Expert's post
from image: a²/4 :?
Director
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 [#permalink] New post 23 Dec 2007, 15:29
walker wrote:
from image: a²/4 :?



Your previous answer seems closer to the actual answer.
Thanks for telling about symbols.
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 [#permalink] New post 23 Dec 2007, 19:23
From image, It also (a^2)/4 for me. Anyway, how could you get D?
Director
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 [#permalink] New post 23 Dec 2007, 19:56
sondenso wrote:
From image, It also (a^2)/4 for me. Anyway, how could you get D?


Yeah, my point is: I am not sure whether I've drawn the image correctly or not? Is image as per the question?
  [#permalink] 23 Dec 2007, 19:56
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