A Circle With Unknown Centre

[Domayele]

“I constructed a circle by tracing around the shape of the base of a good cylinder(such as Milk Tin):

How can the centre of such a circle be obtained, in order to measure its radius?

IN SUMMARY:

How Can an Unknown Center of a Circle be Located?

NB:

With only a straight edge and a pair of compasses.

[Radical Edward]

don't you have a set square?

 

draw a tangent on one side, and one on the other, parallel to the first. check they are parallel using the ruler (since you can extand the lines as far as you like) and then you have the diameter. hald that and you have thee radius.

[Radical Edward]

if you have a set square it is alot easier, since you automatically have a right angle there, which you can arrange on the circle to get your tangents.

[YT2095]

or find the widest point with your rule and divide it by 2

[fafalone]

..or just guestimate... accurate enough.

[Radical Edward]

take the compass and keep enlarging it until it touches the other side might be another way of doing it.

[DimShadow7]

Using the ruler, draw a line that crosses the circle at two points (A and B). Take the compass and put it on point A, and then extend the compass past the center (you'll have to guess the approximate center for this), now draw and arc. Then take the compass, keeping it open the same exact distance, and place it at point B, and draw another arc. The two arcs should cross in two places. Take a ruler and and connect the two points. This should also cross the original line AB, and that point will be the center of the cirlce.

[Domayele]

Thanks DimShadow7 & Co...

For Your Replies!

[YT2095]

why do most all of the answers here take the complex route though?

using a simple rule will do the job

(yes it`s a rule not a ruler!)

take the widest part (diameter) and divide by 2, that will be the middle

 

nothing fancy, just plain old boring common sense

[jordan]

why do most all of the answers here take the complex route though?

using a simple rule will do the job

(yes it`s a rule not a ruler!)

take the widest part (diameter) and divide by 2' date=' that will be the middle

 

nothing fancy, just plain old boring common sense [/quote']

 

The point of most of these exercises is creative thinking and finding exact methods. Finding the intersection of arcs and lines is much more mathematicly accurate than guessing the middle and dividing by two, escpecially when it was specified that a compass may be used.

[YT2095]

for a start who mentioned Guessing? and secondly why make excessive work for yourself when finding the diameter and dividing by 2 to find the radius (and therefore center) using only a rule and a modicum of common sense will suffice?

 

creative thinking ??? LOL, how could you get more creative than that???

 

[edit] you said may be used... MAY BE (as in not essential)!!!!

[jordan]

for a start who mentioned Guessing?

 

Your right, no one did. I thought of taking that word out but I didn't. I only used guessing becuase lining a ruler up and trying to eye when it is the widest isn't really a mathematicly sanctioned method. For these instances it might work, but in the greater picture it wont.

 

and secondly why make excessive work for yourself when finding the diameter and dividing by 2 to find the radius (and therefore center) using only a rule and a modicum of common sense will suffice?

 

Because it's the greater principle at stake here. Yes, I know this seems a bit over-done, but I am a firm believer in learning principles. Experience with other students has led me to believe that those who don't understand basic principles have difficulty grasping more complex ones. In this case it is the act of using a compass and intersecting arcs I think they are trying to get at.

 

creative thinking ??? LOL, how could you get more creative than that???

 

Everyone's first reaction would be to just measure it and divide by two. The creative ones are the ones like DimShadow7's.

 

 

[edit'] you said may be used... MAY BE (as in not essential)!!!!

 

True, but like I said before, if it is said that you could use a compass, that is a pretty clear indication that one's answer should include the use of a compass.

 

 

All together, YT, I agree that yours is a valid answer. You asked why everyone made it so complicated, and I am just trying to explain why.

[Crash]

Heres my method, works 100% and is relatively easy if you get the gist of it

[Freeman]

Put a line anywhere that goes through the circle. Use a protractor to get the perpindicular bisector and extend it through the circle. Find the center of that line, and THAT is the center of the circle.

 

I was a pizza dude and I wanted to put the funky table in the EXACT center, and that was my formula.

[mossoi]

Measuring the diameter and dividing by two won't be very accurate. You need to be sure that the line crosses exactly through the centre of the circle. The summary of the question asked how to locate the centre or a circle of unknown radius as well as how to find the radius. Even if you had the radius already it's still gonna be hit and miss measuring to the exact center of the circle.

 

I was a pizza dude and I wanted to put the funky table in the EXACT center, and that was my formula.

Do you reckon any of your customers appreciated this extra effort?

[senexa]

Use a protractor or compass to measure three points on the circumference of the circle, 120 dg apart. Draw a line from each toward the center, where they meet is the true center.

[mossoi]

Same problem with this as measuring the diameter. You may have three lines starting at accurate points around the circle but how will you ensure your lines are exactly perpendicular to the tangent of the circle?

 

A better way would be to use the same method but mark 6 points (60 degrees apart) and connect opposing point. That way you'll be sure that your start and end points are accuractely marked.

 

Personally I would fold the paper in half carefully with a sharp crease so that the two semicircles exactly match, open it up and then do the same again with the circle rotated (doesn't matter how far as long as you get two lines). Where the lines cross is the centre. Repeat this several times to be sure of accuracy. If the circle is drawn on a none circular piece of paper (hasn't been cut out) just make sure the circumference is drawn nice and thick and hold it up to the light as you fold.

 

Hopefully this satisfies the criteria for both accuracy and simplicity that's being debated.

 

Edit: You can even use the straight edge and compasses to score the folds to get extra brownie points for using the suggested equipment

[Freeman]

Measuring the diameter and dividing by two won't be very accurate. You need to be sure that the line crosses exactly through the centre of the circle. The summary of the question asked how to locate the centre or a circle of unknown radius as well as how to find the radius. Even if you had the radius already it's still gonna be hit and miss measuring to the exact center of the circle.

Well, no. If you have a circle, then have a line go through the circle, through any two points on the circle, in one end and out the other, i.e. NOT TANGENT, then you could find the center of that line with a protractor measured at the length of the line, put on one end then measure above and below the line and do the same on the other point. The two hemi-circles will intersect and use your handy straight edge to make a perpindicular bisector, this is the diameter. Then, find the center of this line with the same method of the protractor, measure above and below, find the perpindicular bisector and THAT is the center of the circle. I call it the freeman theorum.

[mossoi]

Yeah. My post was in response to YT's method.

[bloodhound]

just take four points ABCD. use the normal process to bisect AB and CD. join up the two bisectors and the point where they meet is the centre

[Dave]

I'm hopeless at this kind of stuff, always hated trying to do stuff with a compass and a straight edge.

 

btw, nice one bloodhound (I seem to be saying that a lot recently )

[bloodhound]

When is was in nepal, our maths syllabus used to spend quite a lot of time covering how to draw triangles with certain specs, rectangles, parralelograms, angles like 60 45 90 125 . bisecting them. etc. so i ve got quite a lot of practice at that sort of work.

 

most of the time u said nice one, i seem to have a mistake in the calculation and it turns out to be a really bad one.

[mossoi]

This will only work if they are exactly positioned over the circle though. Dimshadow has supplied the correct method.

[bloodhound]

i dont understand mossoi. the one i posted is basically the same one as by dimshadow. except instead of drawing a line crossing at two points A and B. i start of at any two points A and B without drawing a line. when u draw an arc which meets at two place above the virual line AB and below AB . its bisects the line AB and the arc AB and its perpendiculat to AB and thus the perpendicular to the tangent at the point where the bisector meets the circle. so if u extend this bisector, it will give u a line along the diameter of the cirlce. if u do this for another CD then it will give u another line along the diameter. and where they cross , its the centre.

 

another practicle way of finding the centre is to hang the circle by a piece of string. extrapolate the line on the circle from the string. do this at another point. and draw another line. the point at which those two lines meeet is the centre.

[mossoi]

I didn't understand the whole method from your first post. That explanation clears it up though - and I agree that it works.

 

The hanging method assumes that the paper is a constant density and that the circle can be perfectly cut out.