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# What is the area of a triangle inscribed in a circle

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Director
Joined: 03 Sep 2006
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What is the area of a triangle inscribed in a circle [#permalink]

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22 Dec 2007, 21:54
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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
CEO
Joined: 17 Nov 2007
Posts: 3585
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
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Kudos [?]: 3983 [0], given: 360

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23 Dec 2007, 01:51
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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Kudos [?]: 895 [0], given: 33

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23 Dec 2007, 07:56
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".

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

untitled.PNG [ 7.89 KiB | Viewed 1454 times ]

CEO
Joined: 17 Nov 2007
Posts: 3585
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 575

Kudos [?]: 3983 [0], given: 360

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23 Dec 2007, 10:16
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)
CEO
Joined: 17 Nov 2007
Posts: 3585
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 575

Kudos [?]: 3983 [0], given: 360

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23 Dec 2007, 10:21
from image: a²/4
Director
Joined: 03 Sep 2006
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Kudos [?]: 895 [0], given: 33

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23 Dec 2007, 16:29
walker wrote:
from image: a²/4 :?

Thanks for telling about symbols.
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23 Dec 2007, 20:23
From image, It also (a^2)/4 for me. Anyway, how could you get D?
Director
Joined: 03 Sep 2006
Posts: 873
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Kudos [?]: 895 [0], given: 33

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23 Dec 2007, 20:56
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?
23 Dec 2007, 20:56
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# What is the area of a triangle inscribed in a circle

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