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Source: — Problem Solving |
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by Prasanna » Tue Aug 14, 2007 3:47 am
ABC is equilateral and this means arc AB=BC=CA. (all the three angles in the triangle =60 degrees). If ABC = 24 we can make out that AB=BC=CA=12 and Circumference Pie D = 36. Which gives D=36*7/22=11.45(Apprx). The answer should be C .

Whats the OA?
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by UmanG » Tue Aug 14, 2007 3:54 am
Hi,

Since it's equilateral triangle length of the arc made by each side will remain same,
i.e. Length of arc AB = Length of arc BC = Length of arc AC....(1)


--> Length of arc ABC = 24
--> Length of arc AB + Length of arc BC = 24
--> 2 * Length of arc AB = 24...........(From (1))
--> Length of arc AB = 12...........................(2)

-->Perimeter of circle = Length of arc AB + Length of arc AC + Length of arc BC
--> 2*(Pi)*(Radius) = 3 * Length of arc AB
-->2*(Pi)*(Radius) = 36...........(From (2))
--> Radius ~= 5.3
--> Diameter ~= 11

Leads to OA - C

Hope it will help..:)
Thanks,
UmanG - restless mind..
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by tanyajoseph » Tue Aug 14, 2007 5:03 am
Great! Thanks for the quick responses.
Gettin skeptical as the dates are nearing! Wish i tune myself well before the d day :-|
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by krishnamurthyu » Tue Aug 14, 2007 5:30 am
Arc length of Inscribed Equilateral Triangle ABC = 2/3 of Circumference of Circle
24 = 2/3 * (2 * PIE * R)
24 = 2/3 * (PIE * D )
24 * 3/2 *1/PIE = D;
24 * 3/2 * 7/22 =~ 12 = Ans.C
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by beny » Tue Aug 14, 2007 12:08 pm
An easier way would be just to educatedly guess. I looked at the problem and guessed the correct solution in 10 seconds.

Each side of the triangle is 8, imagine a diameter that connects with one vertex of the triangle (and thus bisects the opposite side of the triagle). Connect the other side of the diameter with the either of the other vertices of the triangle to create a new triangle. 1 side of the new triangle is 8, the other side is obviously significantly smaller than 8 (no way is the new side equal to 7), so the diameter can only be 11.


Sorry for any typos. I'm currently stuck in Seoul Airport trying to get back to the States... can't use a Korean keyboard.
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