The points A,B and C lie on a circle that has a radius 4. If

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The points A,B and C lie on a circle that has a radius 4. If [#permalink]

20 Jun 2006, 05:35

The points A,B and C lie on a circle that has a radius 4. If the length of the arc ABC is 4pi/3, what is the length of line AC?

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20 Jun 2006, 05:53

Full circle is 8pi
4pi/3 is 1/6 of full circle = 60 degrees
therefore angle AOC is 60 degrees, and as OA=OC=4 (being both radii) the triangle AOC is equilateral -> AC = 4

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Re: Length of line segment [#permalink]

20 Jun 2006, 07:55

positive soul wrote:

The points A,B and C lie on a circle that has a radius 4. If the length of the arc ABC is 4pi/3, what is the length of line AC?

Circumference of circle -= 2*pi*r = 8*pi;
=>Slice of circle = (4*pi/3)/(8*pi) = 1/6
=> angle between center and arc =(1/6)*360 = 60 degrees.
Since OA and OC are 4 (radius), the other 2 angles are also 60 degrees. So the triangle is equilateral => AC = 4.
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20 Jun 2006, 10:18

AC = 4, as s= r x Angle = 4 x pi /3
Angle = 4xpi/3x4= pi/3 = 60 degrees

Therefore this is an equilateral triangle.
AC = OA =OC = 4

[#permalink] 20 Jun 2006, 10:18

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The points A,B and C lie on a circle that has a radius 4. If

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The points A,B and C lie on a circle that has a radius 4. If

The points A,B and C lie on a circle that has a radius 4. If

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