ok, I know there are other ways to do this that are much more straight forward but I'm hell bent on using an equation.
Right now I'm making a tactics BS that is radius based. In order to keep the entity from going out of bounds of the circle I have an equation that checks his position in relation to the center of the circle.
Basicly: sqrt( (x-h)^2 + (y-k)^2 )= r
I've developed an equation that will keep the character on the same slope and just put him back where he belongs.

x={2h+ sqrt[ 4h^2 +4(1+s^2)(k^2+r^2+h^2) ] }
/ [ -2(1+s^2) ]

That equation was made from the fact that
the slope s=y/x
and
y= sqrt[ r^2 - (x-h)^2 ] +k

thus:
s= { sqrt[ r^2 - (x-h)^2 ] +k } /x

solve for x and you get my uber equation. After I've found x I can plug it into:
y= sqrt[ r^2 - (x-h)^2 ] +k

-------
Now as far as I can tell, it all works. Unfortunately, because verge doesnt deal with decimals, I have to 'bitshift?' I think they call it? I dunno... basicly:
s is less than or equal to 1 and I need to make it *100 and compensate so I get the same answer for y

sure.
the equation is for a tactics system where the player can move within a circle. If the player tries to go out of the circle, I need to push him back into the circle.

Currently I have a working method thats basicly:

while(entity is outside circle){
x--;
y--;
}

but I cant stand using that because its very shoddy and I know I can use an equation to simply put him in his place.
thus why I made the equation for finding X.

the slope is simply the relationship between x and y. its a way of keeping the angle with the circle the same. In math class they probably refered to it as rise/run or y/x. By using the slope in my equation I can find just x with out knowing the y. And obviously when I find x, I can easily find y.

Ex:

circle_x=5
circle_y=7
circle_r=10

ent_x=20
ent_y=13

slope=ent_x/ent_y

what is the maximum ent_x and ent_y can equal in order to have the same slope and be within the circle?

using my equation I get:
ent_x=5.85
ent_y=16.96

--------
NOW -ASSUMING- that all my math is flawless, I need to integrate the equation into verge. probelm=verge doesnt do decimals. slope is going to be in decimals and the x and y values might need to be rounded. thus my problem.

AHHH! how are you supposed to use atan without being able to use decemals!? -_-

I just had to point out that you are talking to yourself.

if(left && (entity.x-circlecenter.x)^2 + (entity.y-circlecenter.y)^2 [IS LESS THAN] radius^2)
go left;
else
unpress(left);

of course, it depends how the rest of your system is set up. Just my 2 cents.

And apparently I can't use less than signs. There you go then.

The command for less than signs is &.lt.; minus the periods (gt for greater than).

I think what you just said up there is what he was trying to avoid because it looks bad.