Problem Statement
In the figure shown below, ABCDE is a regular pentagon and AG=1. What is FG+JH+CD?
[asy]
import cse5;pathpen=black;pointpen=black;
size(2inch);
pair A=dir(90), B=dir(18), C=dir(306), D=dir(234), E=dir(162);
D(MP("A",A,A)--MP("B",B,B)--MP("C",C,C)--MP("D",D,D)--MP("E",E,E)--cycle,linewidth(1.5));
D(A--C--E--B--D--cycle);
pair F=IP(A--D,B--E), G=IP(B--E,C--A), H=IP(C--A,B--D), I=IP(D--B,E--C), J=IP(C--E,D--A);
D(MP("F",F,dir(126))--MP("I",I,dir(270))--MP("G",G,dir(54))--MP("J",J,dir(198))--MP("H",H,dir(342))--cycle);
[/asy]
<spanclass=′latex−bold′>(A)</span>3<spanclass=′latex−bold′>(B)</span>12−45<spanclass=′latex−bold′>(C)</span>35+25<spanclass=′latex−bold′>(D)</span>1+5<spanclass=′latex−bold′>(E)</span>1011+115