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

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Manager
Joined: 24 Oct 2005
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The points A,B and C lie on a circle that has a radius 4. If [#permalink]  20 Jun 2006, 04:35
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?
VP
Joined: 15 Jun 2006
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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
Director
Joined: 07 Jun 2006
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Re: Length of line segment [#permalink]  20 Jun 2006, 06:55
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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VP
Joined: 02 Jun 2006
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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
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