restart;
with(plots):
# Warning, the name changecoords has been redefined
x:=a*(t-sin(t));

y:=a*(1-cos(t));

a:=2;

P1:=plot([x,y,t=0..2*Pi]):
display(P1);

a:='a';

x2:=a*(t-(1/2)*sin(t));
y2:=a*(1-(1/2)*cos(t));


a:=2;

P2:=plot([x2,y2,t=0..2*Pi]):
display(P2);

display(P1,P2);

L2:=a*int(sqrt(5/4-cos(t)),t=0..2*Pi);

evalf(L2);

a:='a';

x3:=(a-c)*cos(t)+c*cos((a-c)/c*t);
y3:=(a-c)*sin(t)-c*sin((a-c)/c*t);


a:=5;
c:=2;


plot([x3,y3,t=0..4*Pi]);

dx3:=diff(x3,t);
dy3:=diff(y3,t);


# Compute only one arc and multiply by 5 to obtain total length
L:=5*int(sqrt(dx3^2+dy3^2),t=0..4*Pi/5);