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by pkw209 » Thu Dec 10, 2009 7:55 pm
Hi all,

Couldn't figure this one out. Would appreciate a brief explanation. thanks!

Diagram-Try and picture a circle with an equilateral triangle inscribed within it (all three points a, b, and c touching the edge of the circle). just want to make sure it's clear :)

Q) In the figure, equilateral triangle ABC is inscribed in the circle. If the length of the arc ABC is 24, what is the approximate diameter of the circle?

1) 5

2) 8

3) 11

4) 15

5) 19
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by papgust » Thu Dec 10, 2009 8:47 pm
I'm not sure whether i'm correctly diagramming it with the given info. In the diagram, I've ignored the arc AC as the length is given only for arc ABC [---Please correct me here if i'm wrong---]

Each angle of the triangle is 60 degrees. So the angle subtended on the arc is 120 degrees [Because the angle at the centre subtended by the arc is 120 (2*60)]. So we have AB as 120 and BC as 120. Totally, 240 degrees.

Now, find the radius of the circle using the formula
Length of arc = Angle of sector/360 * 2 * pi * r

We know that length of arc ABC is 24 and arc ABC is 240 degrees.

24 = 240/360 * 2 * pi * r
r = 18 / pi

Therefore, diameter of a circle = 2 * 18/pi = 11 (Approximately)

Choice C.
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by thephoenix » Thu Dec 10, 2009 9:42 pm
IMO C

equilateral triangle inscribed in circle will break the circle in three equal arc length

since arc length of ABC is 24 , therefore each arc is 12 and cicumference of circle is 36

now 2 pi r=36
---> d=2r=126/11=approx 11
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by pkw209 » Fri Dec 11, 2009 11:58 am
you guys are both correct! the answer is c. thank you!

Careless errors always hurt me :(
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