Finding the middle of a circle

Jakko

SMF Poster
Joined
Apr 28, 2018
Messages
967
Likes
455
Points
63
First Name
Jakko
#1
Important Note: The method I explain below only works because I happened to get lucky drawing the triangle. See further down this thread for a way that does actually work

I needed to saw a disc (actually a wargames base) in two equal halves, but it didn’t have a clear centre point visible on it.

IMG_2704.jpg

Here’s how to do it. First, draw a triangle whose points are on the disc’s circumference:

IMG_2705.jpg

Make this as large as you can, meaning it’ll be approximately equilateral — though there’s no need to make the corners exactly 60°. Just eyeballing it will be accurate enough. (You could draw the triangle much narrower, but you’ll make things easier for yourself if you don’t :smiling3:)

Next, from each of the triangle’s corners, draw a line that’s at a 90° angle to the opposite side:

IMG_2706.jpg

These three lines should all cross the same point: the so-called orthocenter of the triangle. Because the triangle’s points are on its circumference, this coincides with the centre of the disc.

In my case I just had to saw straight through that to get two halves:

IMG_2707.jpg

but you could of course also use it to drill a hole for an axle, glue something dead centre, or for anything else that requires you to find the middle of a circle.

(With the added note that for cutting a disc in halves, you don’t even need to draw six lines: three will do. Draw two sides of the triangle and then the third line from one of the “open” corners to the line opposite. This will go through the centre of the disc if you do it right. It’s just that it’s easier to spot errors if you do draw all six lines, because you can see whether the ones in the middle all go through the same point.)
 
Last edited:

Jim R

SMF Poster
Joined
Apr 27, 2018
Messages
1,155
Likes
882
Points
113
First Name
Jim
#3
I have just learned something simple and useful which I didn't know before :thumb2:
Thanks
Jim
 

Ian M

GB Mod
Administrator
Moderator
Joined
Dec 14, 2008
Messages
11,692
Likes
2,011
Points
113
Location
Falster, Denmark
First Name
Ian
#4
Or you take a set square and a 45 degree angle. Place the disk or rod in the 90deg angle then place the 45deg so it bisects the angle draw a line, turn the disc and repeat..
 

Gern

'Stashitis' victim
Joined
May 17, 2009
Messages
5,217
Likes
1,708
Points
113
Location
Stourbridge
First Name
Dave
#5
I needed to saw a disc (actually a wargames base) in two equal halves, but it didn’t have a clear centre point visible on it.

View attachment 298589

Here’s how to do it. First, draw a triangle whose points are on the disc’s circumference:

View attachment 298590

Make this as large as you can, meaning it’ll be approximately equilateral — though there’s no need to make the corners exactly 60°. Just eyeballing it will be accurate enough. (You could draw the triangle much narrower, but you’ll make things easier for yourself if you don’t :smiling3:)

Next, from each of the triangle’s corners, draw a line that’s at a 90° angle to the opposite side:

View attachment 298591

These three lines should all cross the same point: the so-called orthocenter of the triangle. Because the triangle’s points are on its circumference, this coincides with the centre of the disc.

In my case I just had to saw straight through that to get two halves:

View attachment 298592

but you could of course also use it to drill a hole for an axle, glue something dead centre, or for anything else that requires you to find the middle of a circle.

(With the added note that for cutting a disc in halves, you don’t even need to draw six lines: three will do. Draw two sides of the triangle and then the third line from one of the “open” corners to the line opposite. This will go through the centre of the disc if you do it right. It’s just that it’s easier to spot errors if you do draw all six lines, because you can see whether the ones in the middle all go through the same point.)
Nice to see a bit of maths! (ex maths tutor). If it's easier for you to do, you don't need to measure the 90 degree angles. Just mark the centre of the side of the triangle and draw from there to the opposite vertex (point of the triangle). The 90 degree line always passes through the centre of the side of the triangle.
 

Jakko

SMF Poster
Joined
Apr 28, 2018
Messages
967
Likes
455
Points
63
First Name
Jakko
#7
Nice to see a bit of maths! (ex maths tutor). If it's easier for you to do, you don't need to measure the 90 degree angles. Just mark the centre of the side of the triangle and draw from there to the opposite vertex (point of the triangle). The 90 degree line always passes through the centre of the side of the triangle.
You made me realise I’ve made a fundamental error, haven’t I? I only got the right outcome because I happened to have drawn a triangle that’s fairly close to being equilateral :sad: With any other kind of triangle, neither drawing a line at 90° to the opposite side, nor drawing it to the center of that side will work (both amount to the same thing in an equilateral triangle, which is why Gern’s method may be simpler than what I originally posted, depending on the tools you have available). However, drawing an equilateral triangle is kind of hard to do on any random circle unless you have a protractor of some kind that’s small enough to let you mark degrees actually on the disc, if you’re working with physical materials.

But then why did I seem to remember that the method I so happily recommended, works with any type of triangle? Anyway, scratch that whole method. Rather, try the following:

Draw a line from one point on the circumference to any other point on the circumference. Measure where its halfway point is, then draw a second line through that at 90° to the first line. This line will cross the centre point of the circle. If you need to cut the disc in half, that’s all you need. If you need the actual centre of the circle/disc, make a mark halfway along the second line.

Here’s a quick illustration:

Schermafbeelding 2018-04-30 om 23.59.34.png
 

Gern

'Stashitis' victim
Joined
May 17, 2009
Messages
5,217
Likes
1,708
Points
113
Location
Stourbridge
First Name
Dave
#8
Methinks you're talking yourserlf out of this Jakko. Your method does work with ANY triangle drawn within a circle. The only thing you have to do is make sure that when you draw your right-angled line from the side of the triangle, it meets the opposite vertex (point) of the triangle correctly.

There's a selection of mathematical proofs that state that any radius of a circle bisects a chord at right angles - you don't need the proof but I thought I'd show off a bit of maths knowledge!:smiling5:
 

Jakko

SMF Poster
Joined
Apr 28, 2018
Messages
967
Likes
455
Points
63
First Name
Jakko
#9
It does? I tried, and couldn’t get it to work with a couple of random triangles (other than an equilateral one) — not with the method I originally posted and not by drawing lines at right angles.
 

John Race

Plastic burner and member of the Rabble
Joined
May 26, 2015
Messages
1,507
Likes
965
Points
113
Location
lincs
First Name
John
#10
All too technical for me. :confused:I'd just measure the dia and divided by 2, but very informative and will note.Thank you .
John
 

monica

SMF Poster
Joined
Oct 30, 2013
Messages
12,419
Likes
5,810
Points
113
First Name
monica
#11
I,m with John,hurts my head this early in the morning ,or just pot luck,:astonished::hugging-face:
 
Joined
Apr 27, 2018
Messages
12
Likes
10
Points
3
First Name
sidney
#12
if the diameter is measured and a compass set to 1/2 D (radius), the center will be the intersection of arcs drawn from any three points on the circumference.

won't it?
 

Gern

'Stashitis' victim
Joined
May 17, 2009
Messages
5,217
Likes
1,708
Points
113
Location
Stourbridge
First Name
Dave
#13
if the diameter is measured and a compass set to 1/2 D (radius), the center will be the intersection of arcs drawn from any three points on the circumference.

won't it?
Absolutely correct, any two arcs drawn that way will give the centre. That's easy if you're drawing on a piece of paper but you might have a problem holding the compass point exactly on the edge of a disc .....
 

Jakko

SMF Poster
Joined
Apr 28, 2018
Messages
967
Likes
455
Points
63
First Name
Jakko
#14
And that’s why using triangles or straight lines and 90-degree angles work better for modelling, at least you’re not working with plastic sheet before you cut the disc from it.
 

Tom Rigg

SMF Poster
Joined
Apr 29, 2015
Messages
92
Likes
12
Points
8
#15
Someone, somewhere posted a link to make a circle center finder (CCF) using a flat base with an isosceles shape made from square plastic glued to it. Mark the middle of the base line.
put the disc into the CCF touching both 'long' sides then lay a ruler from the apex to the middle mark and draw a line on your disc. Turn the disc by 90 degs and repeat. It works for smaller diameters really well especially when you need lots of discs.
I'll try and find the post and link it.
Tom
 

wasdale32

SMF Poster
Joined
Apr 27, 2018
Messages
7
Likes
8
Points
3
First Name
Mark
#16
Might sound too obvious - but why not draw round the circular object on a piece of paper, cut it out then simply fold the paper in half - if you then measure the diameter and halve it then you get the centre....

or fold it twice and you get a quarter circle with the point at the centre

Mark
 

spanner570

SALAD DODGER
Moderator
Joined
May 26, 2009
Messages
6,996
Likes
3,127
Points
113
First Name
Ron
#17
Might sound too obvious - but why not draw round the circular object on a piece of paper, cut it out then simply fold the paper in half - if you then measure the diameter and halve it then you get the centre....

or fold it twice and you get a quarter circle with the point at the centre

Mark
Mark, you beat me to it. I've always used that method. No faffing about. Quarter circle is best.....There again I'm only a thick retired Joiner, so back in my work days I had to have something to hand that was simple and fool proof every time!
 

Jakko

SMF Poster
Joined
Apr 28, 2018
Messages
967
Likes
455
Points
63
First Name
Jakko
#18
Might sound too obvious - but why not draw round the circular object on a piece of paper, cut it out then simply fold the paper in half - if you then measure the diameter and halve it then you get the centre...
Because it’s more work for the same result? :smiling3:
 
Top