How do I create an offset shape that is a specific distance from a given circle, in the direction of the origin? I'm an amateur engineer, working on a CAD design - but sadly, I'm not a mathematician.
In other words, this question might sound like homework, but it's not, I promise.
I have an existing circle, which has a radius of $23.5$ with the center point being $(0,15)$
I need to write an equation ($s$) which I can input into my CAD software (i.e. no calculus, but algebra is OK), which will draw a continuous shape that is smaller than the existing circle, but is always the EXACT same distance ($d$) away from the circle, when measured across ANY line that passes through the origin $(0,0)$
I think the resulting shape ($s$) should NOT be a smaller circle.
It should be an odd shape of some kind, maybe an ellipse or egg or some other type of squished circle?
But that's as much as I know.
I have no idea where to even begin solving this, my trigonometry is way too rusty ...


The equation of the circle is $(x,y)=(r\cos\theta,a+r\sin\theta)$. The question is for the curve $s(x,y)$ such that $(1-s)|(x,y)|=d$. Solving this gives $s=1-\frac{d}{\sqrt{x^2+y^2}}$.
Hence the curve is given by the pseudo-code:
r=23.5; a=15;
x(t):=r*cos(t);
y(t):=a+r*sin(t);
s(t):=1-d/sqrt(x(t)^2+y(t)^2);
plot((s(t)*x(t),s(t)*y(t)),(t,0:2*PI))

