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An equilateral triangle ABC is inscribed inside a circle

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An equilateral triangle ABC is inscribed inside a circle [#permalink] New post 01 Feb 2007, 04:14
An equilateral triangle ABC is inscribed inside a circle (such that each vertex touches the circle - ie. fits perfectly). Length of the arc ABC is 24.
What is the approx. diameter of the circle?

Choices: 5 8 11 15 19
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 [#permalink] New post 01 Feb 2007, 09:43
The answer is 11. As the triangle is equilateral the arc ABC covers 2/3 of the cricumference of the cirlce and hence the remaining arc AC is 1/3 of the circumference going by that logic 2Pir = 36 and hence 2r = 11. I hope this helps.
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 [#permalink] New post 02 Feb 2007, 08:02
successstory, can you verify if 11 is the answer?
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 [#permalink] New post 02 Feb 2007, 13:47
See attached picture below,

We know that "Arc of segment = angle of segment x radius" or S = @r

In this case radius is constant because we calculate in the same circle.

S is proportional to @
Thus, S1/S2 = @1/@2

S1/24 = 360/240 {360 is the angle of the whole circle, 240 is the angle of the segment ABC)
S1 = 36

And, Circumferenc = Pi x Diameter

36 = Pi x Dia.
Dia. = 36/Pi or Approx 11.4

The answer is 11.
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circleAns.jpg
circleAns.jpg [ 31.85 KiB | Viewed 661 times ]

  [#permalink] 02 Feb 2007, 13:47
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