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

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Director
Joined: 03 Sep 2006
Posts: 885
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Kudos [?]: 256 [0], given: 33

What is the area of a triangle inscribed in a circle [#permalink]  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
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 406

Kudos [?]: 2133 [0], given: 359

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
Joined: 03 Sep 2006
Posts: 885
Followers: 6

Kudos [?]: 256 [0], given: 33

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?

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

untitled.PNG [ 7.89 KiB | Viewed 800 times ]

CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 406

Kudos [?]: 2133 [0], given: 359

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?

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: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 406

Kudos [?]: 2133 [0], given: 359

Expert's post
from image: a²/4
Director
Joined: 03 Sep 2006
Posts: 885
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Kudos [?]: 256 [0], given: 33

walker wrote:
from image: a²/4 :?

SVP
Joined: 04 May 2006
Posts: 1936
Schools: CBS, Kellogg
Followers: 19

Kudos [?]: 433 [0], given: 1

From image, It also (a^2)/4 for me. Anyway, how could you get D?
Director
Joined: 03 Sep 2006
Posts: 885
Followers: 6

Kudos [?]: 256 [0], given: 33

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?
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