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# geometry

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Intern
Joined: 20 Feb 2012
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12 Mar 2012, 14:16
how to find the length of arcs of circles at the vertices. for example in the figure if radius of circles is given. how to get length of major arcs?

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Joined: 12 Sep 2011
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12 Mar 2012, 17:00
Could you clarify the question slightly?

If what I understand is correct, you are trying to find the length of the arc of the circles that are located inside the triangle? If this is the case, you would need to know the angles of the vertices of the triangle. For example, lets say your picture is an equalateral triangle (all angles are 60), then to find the length of the arc you would have to be atleast given the radius of the circle and know that the vertices of the triangle lie in the center of the circles. Once you have the radius you would use the formula: 2(pi)r to get the circumference, and that you would multiply the circumference by 60/360 (b/c this is the portion of the circumference of the circle within the 60 degrees of the triangle).

For example, if the radius of the circle was 1, then the circumference of the circle would be 2(pi). You'd multiply the 2(pi) by 60/360 (aka 1/6) to get the length of the arc of 1/3(pi) inside the triangle. If you are looking for the arc length on the outside of the trinable then you would have instead multiplied the 2(pi) by 300/360 to get 1 and 2/3(pi)

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Re: geometry   [#permalink] 12 Mar 2012, 17:00
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