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We start with a given circle.

Geometry construction with compass and straightedge or ruler or ruler
1.  Place the right-angle corner of any object at any point on the circle. Any point will do. Geometry construction with compass and straightedge or ruler or ruler
2.  Make a mark where the two sides of the right-angle cross the circle. Geometry construction with compass and straightedge or ruler or ruler
3.  Draw a line between these two marks. Because of Thales Theorem, this is a diameter of the circle. Geometry construction with compass and straightedge or ruler or ruler
4.  Place the right-angle corner of the object at any other point on the circle. Any point will do, but for greatest accuracy, make it about a quarter the way round the circle from the first point. Geometry construction with compass and straightedge or ruler or ruler
5.  Make a mark where the two sides of the right-angle cross the circle. Geometry construction with compass and straightedge or ruler or ruler
6.  Connect these two points with a straight line. This is the second diameter. Geometry construction with compass and straightedge or ruler or ruler
7.  Done. The point where the two diameters intersect is the center of the circle. Geometry construction with compass and straightedge or ruler or ruler

Why it works

Geometry construction with compass and straightedge or ruler or rulerThis method works as a result of Thales Theorem. The diameter of a circle subtends a right angle to any point on the circle. The converse is also true: A right angle on the circle must cut off a diameter. By finding two diameters, we find the center where they intersect

Visit Thales Theorem for an animated description of how this works.

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...Or you could make a paper pattern and fold in half!!!! But that would be no fun lol!

Awesome!  Thanks Ted


Ted Crocker said:


Fold it in quarters you mean to get center...  


Wade said:  

...Or you could make a paper pattern and fold in half!!!! But that would be no fun lol!

 


Or you can just use a centering jig...

centering jig, seen from the top.same jig seen from below.

I'm making a few dozen spool clamps, so having a way to quickly and accurately find the center of a dowel is a big plus.

what if the dowel is oblong and not perfectly round?
anybody know how find the center of an egg shaped dowel?
i take a pencil between my finger and thumb, point close to the fingers. then use my other fingers as an edge guide and twist the dowel till i get a very small circle like this ( o ) then center punch it. really quick really easy and works on irregular dowels.

Here is another way to find center with a cumpus. Just click on the video at this link. This is the way our shop teacher taught us many years ago.

http://www.mathopenref.com/constcirclecenter.html

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