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> Triangle In A Circle
Jimthecopierwrench
Posted: August 01, 2014 09:18 am
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I want to mark 3 equally spaced points on the edge of a circle.

I figure the best way to do this is draw an equilateral triangle in the circle - figuring that there orta be a simple formula for figuring out one side (length) of the triangle from the circle's known diameter, and that that length will simply give two of the three points simply by contacting the edge of the circle - and of course the third from either of those two.

Found lots of formulas to get a circle in a triangle (and a few like cos30=x/r that seem odd), but not the other way ... anyone know what it is?

Surely this can't be more involved than a bit of pi r over this or that.





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Sch3mat1c
Posted: August 01, 2014 09:30 am
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Technical word is "inscribed" if it's adding the triangle, or "circumscribed" if it's adding the circle.

Offhand:

- Draw a radius of the circle. Presumably, you already know the center point of the circle, so put a point on the circle and draw that line segment.
- The center of the circle is also the center of the triangle, so we know that relates to its size somehow. Probably exactly half. So let's draw an arc segment, centered on the point on the circle, drawn through the origin, and intersecting the circle in two points (i.e., put the compass point on the circle, pencil on its center, and give it a swing).
- Repeat the process, starting from each new intersection, until you're all the way around. Now you have six points on the circle, and you have two choices to pick three to make a triangle. Since that triangle is made of points touching the circle, we have succeeded in inscribing a triangle; and if you picked every other point, it's equilateral too.

Presuming that, by "marking", you mean a classical geometric "compass and ruler" type construction is ideal.

Tim


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Jimthecopierwrench
Posted: August 01, 2014 10:02 am
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QUOTE
so we know that relates to its size somehow. Probably exactly half.
So the exact center of any one side of the triangle will pass through a point half the radius? That's tidy.

QUOTE
Presuming that, by "marking", you mean...
Not in this case. it's a wheel getting moon treatments. I suppose I can come close enough to the true center (a press in 3" grease cap) by eye, but there are large axial depth variations (it's obviously not flat) which don't make bisecting very easy. I was hoping for something I could plug in and come up with a length of (say) welding rod which would be one side of the triangle.

I suppose with a circumference of uh, 50.27" which gives three near 16-3/4" points I might eyeball it around the outside with a tape measure...

An eighth off will not cause a mechanical issue - but it'll mean that each piece will end up married to a particular wheel in a specific orientation.


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Sch3mat1c
Posted: August 01, 2014 10:57 am
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Oh, by length it should be dia / sqrt(3) or something like that.

Tim


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CWB
Posted: August 01, 2014 12:21 pm
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a single or couple of rulers/yard sticks placed across the maximum distance across the rim at 90 degrees (protractor or carpenters angle) will provide the ONC ... it will also provide four reference points from which you can apply tim's method(s) .

string and tape can be your friend .


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jim currie
Posted: August 01, 2014 04:10 pm
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without delving into trig heres a easy way http://www.youtube.com/watch?v=eWtrxXe_yEs
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deth502
Posted: August 01, 2014 08:31 pm
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i assume your using a compass and a straightedge.

draw your circle with your compass. dont lose your center point, your going to need that.

now draw a line through that center point to any point on the circumfrance of the circle where you want one point to be (a). that line is the diameter.

now, use your compass, again, still set to the exact same size. put the point of the compass on the point where your diameter line meets your circle, the one acros from where you want the point. draw 2 lines where it intersects the circle (b+c).

connect those 3 points and you have a perfect equilateral triangel inside your circle
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deth502
Posted: August 01, 2014 08:39 pm
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here is a horrible, horrible ms paint explanation in 3 steps.

user posted image
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deth502
Posted: August 01, 2014 08:48 pm
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just read your follow up post, you could always just draw it out using the method above full scale and make some measurements.
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CWB
Posted: August 02, 2014 02:13 am
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hey , i just realized that i am familiar with a "triangle in a circle" .

so jimmy , are you going to make AA hubcaps ?
laugh.gif


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Jimthecopierwrench
Posted: August 02, 2014 03:09 am
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Yeppers. Flush an aluminum disc right up to the safety bead and secure it with three stainless 1/4-20 allens into tabs welded and drilled to hold threaded inserts.


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jim currie
Posted: August 02, 2014 03:13 am
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or is this what your wanting PIxD/3
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