## Equations for finding points on a circle circumference

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
Bigus
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Joined: Thu Jul 18, 2013 8:42 pm
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### Equations for finding points on a circle circumference

Hi

In this diagram, the points with a green dot are known and the red ones unknown. Could someone explain what formula I need to determine the red dotted points?

Thanks

little_dragon
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### Re: Equations for finding points on a circle circumference

if lines are straight vert/hor then u can use 1/2 of green pts to get red pts
if "known" means "x,y pts" then u can use coords
if center is put to origin then u can use x^2+y^2=r^2
like: for pt c on vert line, u know x-coord for c is same as for l & g (say L)
then y-coord is r^2-L^2
same way for hor lines

jg.allinsymbols
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Joined: Sat Dec 29, 2012 2:42 am
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### Re: Equations for finding points on a circle circumference

Not possible. We do not have the distance relationships for the nine most-central green points in regard to distance from center point to green point on the circle. For example, how does AF relate to FK ? The point F is not the mid point of those. It may LOOK like it, but we are not given that specifically.

... On the other hand, if we can take it that F is a midpoint of AK, then we have something. We might assume the circle is r radius so we have x^2+y^2=r^2, and if we just assign a number or know a number for r, then from the center of the circle, we can read x or y coordinates and calculate the other coordinate. Then we have whatever red point on the circle we want.

Imagine r=1, and KC=1, and KL is 1/2. You then have x=1/2. You could find y.
y^2+(1/2)^2=1
$y^2+(1/2)^2=1$
$y=sqrt(1-(1/4))$

Bigus
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Joined: Thu Jul 18, 2013 8:42 pm
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### Re: Equations for finding points on a circle circumference

Hi

Ahh, so the technique is to use pythagoras - I should have thought of that!

I have extended the formula to deal with the fact that the origin (a,b) of my circles are not 0,0 so to get the y coord for my point C I am using:

$y = b +/- sqrt{r^2 - (L-K)^2}$

(where points on my circle diagram are captalised)

Many thanks for both your help

Regards
Bigus