Question: delete specific parts of my graph

From this program

S1:=unapply(u*FresnelS(u)+((1/Pi)*cos((1/2)*Pi*u^2))-(1/Pi),u);

C1:=unapply(u*FresnelC(u)-((1/Pi)*sin((1/2)*Pi*u^2)),u);

R1:=1;

u1:=evalf(sqrt(0.4));

E1:=evalf(Pi*R1*S1(u1)+R1);

D1:=evalf(Pi*R1*C1(u1)+1);

a:=evalf(Pi*R1*(u1));

with(plottools);

with(plots);

c1 := circle([D1,0], R1);

display(c1);

plot([a*FresnelC(u),a*FresnelS(u),u=0..u1]);

p1:=plots[display](plot([1+a*FresnelC(u),a*FresnelS(u)-E1,u=0..u1]),c1,scaling=constrained);

p2:=plot(-1.064877386,x=0..1);

p3:=plot(1.064877386,x=0..1);

p4:=plots[display](plot([1+a*FresnelC(u),-a*FresnelS(u)+E1,u=0..u1]),scaling=constrained);

c2 := circle([-D1,0], R1);

p5:=plot(-1.064877386,x=-1..0);

p6:=plot(1.064877386,x=-1..0);

p7:=plots[display](plot([-1+(-a*FresnelC(u)),a*FresnelS(u)-E1,u=0..u1]),scaling=constrained);

p8:=plots[display](plot([-1+(-a*FresnelC(u)),-a*FresnelS(u)+E1,u=0..u1]),scaling=constrained);

display(p1,p2,p3,p4,p5,p6,c2,p7,p8);

 

From the displayed graph I am looking to delete the parts inside the 4 points where the curves meet the circles, so I simply have have one long track with nothing inside it.

 

Any ideas?

 

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