How to extrapolate a circle from a line segment

I didn’t take geometry. Nurses need algebra and simple math, no circles.

I’m making a piece of stained glass that has circles. I have some that someone else started a few years ago. I know they aren’t really round.

Here’s what I did, since I have no idea how to go about it mathmatically.

I drew the line segment from a place on the glass that looks right onto tracing paper. I then moved the line so it matched until I had a circle. To check it, I folded the paper so I could see if both sides matched. Then to transfer it to a pattern I poked pin holes through to the pattern paper. It took forever, well, at least a long time.

I have 8 or 9 more to do and I’d rather be able to do it a little faster.

Please make the instructions as simple as possible, I have fairly poor spacial sense.


If I understood the question correctly…

From here:

Draw a line connecting the ends of the arc. Its length will be W (width). Measure the distance from the line to the top of the arc. This will be H (height).

Radius = (Height / 2) + (Width squared / 8H)


R = (H / 2) + (W[sup]2[/sup] / 8H)

There is a calculator on the webpage.

You want a circle with that line segment as diameter? Do you have a compass?

Without a compass you can get quite close doing as follows (assuming your line segment is the diameter and the circle is small enough):

Fold the ends of the line together to find the middle of the segment. Hold a pen and place the tip at one end of the line. Put your index or little finger on the center of the line. While keeping that finger on the center, preferable pressing down a little, turn the paper with your other hand, trying to not change the distance between the tip of the pen and your turning point finger.

ETA: Ah, you transfered part of an arc. That makes more sense.

I’m very confused as to what you’re trying to do, but if you have a radius and you’re trying to make a circle, don’t free hand it, go buy a compass, set it to the line segment (or half of it* depending on if it’s the radius or diameter) and use that. Also, you can just use the compass to get the size right off the glass instead of making that first transfer to the tracing paper.
*C’mon, you remember how to bisect a line segment, right.

Ok, sorry. I need to draw a circle and I have just a small part of that circle. I have a curve that I want to extend into a circle.

I guess I know even less about geometry than I thought.

The project is a glass panel that has a stylized version of the solar system. So, I need several different sizes of glass circles. I have several that my husband started but never finished.

I just need to be able to make patterns for those pieces of glass to be sure they’re round.

That’s called an arc, what you need to do is find that radius from the arc.
Draw a line from one end to the other (you’ll need it), measure how long the is, that’s W, measure how high it is from the line to the top of the arc (the highest point, make sure the ruler is at 90 degrees), that’s H, plug it into this formula).

If you’re not good with order of operations, bring the numbers back and I/we can do it, also, it wouldn’t kill you to get another one or two cites, probably two cites (since you’ll get mine first) on that formula, it might be made up by some crazy person.

That formula spits out R. Draw a dot, draw another dot R units* away, set your compass to that and you’ve got your circle.

*use the same units here that you first measured the arc in, mm, cm, inches, whatever, just don’t change them.

Also, I don’t know how big of a circle you’re working with, but if this is at least a few inches in diameter, you can make this with some string instead of running out to get a compass.

Sounds like you’re gonna need a compass.

Or second. :stuck_out_tongue:


Mark two points on the arc, connect them with a straight line, find the midpoint of this and draw a straight line across it at right angles. Repeat with either of the points and a third one. The two straight lines you have drawn will cross at the centre of the circle. Apply compasses, checking that you are following the arc, and carry on from there. The further apart you can get the points, and the more accurately you can measure your midpoints and right angles, the better. Also pair up your third point with whichever point you didn’t use in drawing your second line, and draw a third line to make sure they all cross at one point.

The string is good. Some are a few inches up to about a foot.

I’m amazed at how easy it was, once explained. All these years (Like 50) I’ve been intimidated by geometry. Well, I still am, but I think I did ok.

Once the project is done, I’ll try to remember to come back and show you.

The string is good. Some are a few inches up to about a foot.

I’m amazed at how easy it was, once explained. All these years (Like 50) I’ve been intimidated by geometry. Well, I still am, but I think I did ok.

Once the project is done, I’ll try to remember to come back and show you.

So the mission was to take the kind of circular glass and to make it a better circle ?

You really just wanted to draw some concentric circles onto the tracing paper,
and find the closest match. eg if its 7" to 8" you expect, draw 7", 7" and 1/4, 7" 1/2, 7" 3/4, 8" …
With this concentric ring tracing paper, you can easily see which parts of the glass is circular and which is curved irregularly (like a part of an oval.) You can also see if the glass is still large enough to make a COMPLETE Circle.

Worried the string method leaves you guessing as to whether the glass is large enough and accurately enough (You can’t stick the string to the glass.)

Also, you can’t draw a good circle with string. Get the compass.

I have a circle glass cutter, but it doesn’t work very well. It’s old and comes apart or slips at the least opportune times. Also, it doesn’t do anything less than about 3 inches.

Isilder, that’s a great idea. I just need to remember to buy a compass.

Oh, and I’d like to apologize for the double post. My computer was being cranky and I couldn’t tell when it actually went. (Did a restart and all is well now)

Malacandra has it right. What you are making is a chord (a segment with endpoints on the circle. The trick is the perpendicular bisector of any chord follows the same path as the diameter. Also, all diameters of a circle meet in the middle so you make two chords, bisect them and the intersection of the bisectors is the middle of the circle. QEF.

Ok, Here’s the first step:
I have the sun and planets, along with Luna. I’m not putting in all the other moons in the solar system, it would be too busy and waay too much work.

As you can see, they are pretty close to round. I got the calculation right, but sometimes the glass just has a mind of it’s own.