Find tangent line to the circle

Hi,

I basically have a circle with given radius and it’s displacement from the origin and now I have to calculate the tangent to the circle at a given point. (Basically if I can get the slope of the tangent it’s ok, I don’t need more).
I did use some google but I couldn’t find an idea how to do this in Mathemathica? :confused:

Any ideas?

is displacement from origin means the coordinates of the center (x0,y0) of the circle? If so, and you know a the coordinates of a given point on the circle say (x1,y1), then why is the radius also given? Not needed, you use use EuclideanDistance to find radius.

But if you know 2 points (x0,y0) and (x1,y1) already, then you can find the slope of this line (the radius). The tangent will be normal to this. So add 90 degrees?

So it is as easy as -(x1-x0)/(y1-y0) ?