Question

Given a circle, what are various interesting ways to find its center ?

Answer 1

Here is one way I am familiar with :
http://www.mathopenref.com/constcirclecenter.html

it uses the fact that the perpendicular bisector of any chord of the circle passes through the center of the circle

Answer 2

I wasnt familiar with even tht one -_-

Answer 3

So in regards to be given a circle, are you provided with any other info about the circle?

Answer 4

Looking at the link, it is basically a construction for locating for the center point

Answer 5

I think not @Miracrown

Answer 6

are you from india ?
if so, these constructions are taught in 8th grade math...
these are not hard but easy to forget yeah :)

Answer 7

@ganeshie8 its bcoz if we draw perpendicular from the centre to the chord...it bisects them ??

Answer 8

Myyy bad I got confused...and now when I think I m so dumb to forget tht .....

Answer 9

here is the actual problem @Miracrown
http://www.euclidea.xyz/en/game/#/packs/Alpha/level/CircleCenter

Answer 10

i don't seem to work it in less than 6 steps...

Answer 11

im sure you're not dumb @rishavraj
it just takes some review to refresh these again in your head :)

Answer 12

lol thts the reason I jst started to give tution classes..... :P

Answer 13

thats the reason i login here frequently too :)

Answer 14

I think I know another method.
Try to draw four tangent lines in the circle to form a square and draw its diagonals..

Answer 15

that is interesting @Yttrium
but the tangent construction itself requires the center to be constructed first right ?

Answer 16

how about folding

Answer 17

you only need two folds

Answer 18

ahh folding works like a charm!
you want to fold twice to get two perpendicular bisectors right ?
i think its still equivalent to 6 steps for euclid...

Answer 19

yeah two perpendicular bisectors

Answer 20

then your method is equivalent to mine, just the tools are different i guess

Answer 21

I'm thinking of one that is not equivalent to yours hmm...

Answer 22

@Yttrium
by triangular ruler you mean the set squares ?
http://www.draftex.com.au/image-optimise.ashx?imageId=1274&imageSize=4

Answer 23

can we use coordinate geometry ?

Answer 24

im wondering if we can somehow use below fact to our advantage
https://i.ytimg.com/vi/eo0_I2jjy6k/maxresdefault.jpg

Answer 25

the coordinate geometry way i think sorta steels @yttrium 's idea of creating a square though
well the one I'm thinking of

Answer 26

I have one that's somewhat similar, but it doesn't require you to construct the chords.
We'll start with a circle. Now, at any point on the circle, I'll use the compass to draw two arcs that are equidistant from that point, for example, from point A:

Answer 27

those two arcs are (supposedly) equdistant from A...
let's call those intersections B and C: