7-2 Construct the line segments joining points of the curve with the corresponding center of curvature for each of the following: the nephroid, the astroid, the deltoid and the cardioid.

> restart:

> x:=3*cos(t)-cos(3*t):y:=3*sin(t)+sin(3*t):

> x1:=diff(x,t):y1:=diff(y,t):

> x2:=diff(x1,t):y2:=diff(y1,t):

> t:=n*Pi/50:

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

> xc:=x-f*y1:yc:=y+f*x1:

> m:=[[x,y],[xc,yc]]:

> w:=evalf(m):

> plot([w$n=1..100],scaling=constrained,axes=none,color=blue);

>