菱形ABCD,P是AC上一点,DP与AB交于点E,BP的延长线与CD的延长线交于点G,与AD交于点F

⑴∵ABCD是菱形,∴AD=AB,∠PAD=∠PAB,
∵AP=AP,∴ΔAPD≌ΔAPB.
⑵则⑴全等得：PD=PD=X,PF=PE=Y,
∵AD∥BC,
∴FG/FB=FD/FA=1/2,PG/PB=PD/PB,
∴FG=1/2FB=1/2(X+Y),(FG+Y)/X=X/Y,
∴Y［1/2(X+Y)+Y］=X^2,
1/2XY+3/2Y^2=X^2,
3Y^2+XY-2X^2=0
(3Y-2X)(Y+X)=0,
∵X+Y≠0,
∴3Y=2X,
Y=2/3X,
当X=6时,Y=4,
∴FG=1/2(X+Y)=5.