> restart:

> x:=cos(t)/(2-(cos(t))^2);

> y:=sin(t)*cos(t)/(2-(cos(t))^2);

> p:=plot([x,y,t=0..2*Pi],color=red,scaling=constrained,axes=none):

> x1:=diff(x,t):

> y1:=diff(y,t):

> x2:=diff(x1,t):

> y2:=diff(y1,t):

> f:=(x1^2+y1^2)/(x1*y2-y1*x2):

> xc:=x-f*y1:

> yc:=y+f*x1:

> r:=(x1^2+y1^2)^(3/2)/abs(x1*y2-y1*x2):

> with(plots):

> b:=animate([xc+r*cos(s),yc+r*sin(s),s=0..2*Pi],t=0..2*Pi,color=blue,scaling=constrained,axes=none,frames=50):

> c:=animate([(1-s)*xc+s*x,(1-s)*yc+s*y,s=0..1],t=0..2*Pi,color=brown,scaling=constrained,axes=none,frames=50):

> display(p,b,c,view=[-1..1,-1..1]);