> restart:

> with(plots):

Warning, the name changecoords has been redefined

> x:=2*cos(t)+cos(2*t):

> y:=2*sin(t)-sin(2*t):

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

> x1:=diff(x,t):

> y1:=diff(y,t):

> x2:=diff(x1,t):

> y2:=diff(y1,t):

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

> xc:=x-f*y1:

> yc:=y+f*x1:

> b:=plot([xc,yc,t=0..2*Pi],axes=none,scaling=constrained,color=yellow):

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

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

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

> display(a,b,c,d);