1999 PMWC Answer Key

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T5. [asy] /* modified Geogebra to Asymptote conversion, documentation at artofproblemsolving.com/Wiki, go to User:Azjps/geogebra */ import graph; size(7cm);  real labelscalefactor = 0.5; /* changes label-to-point distance */ pen dps = linewidth(0.7) + fontsize(15); defaultpen(dps); /* default pen style */  pen dotstyle = black; /* point style */  real xmin = -3.026023412800261, xmax = 8.06690599900684, ymin = -4.726758813006724, ymax = 3.611932987992014; /* image dimensions */ /* draw figures */ draw(circle((0,0), 1));  draw(circle((2,0), 1));  draw(circle((4,0), 1));  draw(circle((1,-1), 1));  draw(circle((3,-1), 1));  /* dots and labels */ label("$2$",(0.5,-0.5));  label("$4$",(1.5,-0.5));  label("$1$",(2.5,-0.5));  label("$3$",(3.5,-0.5));  label("$9$",(-0.207106781186548,0.207106781186548));  label("$8$",(4.207106781186548,0.207106781186548));  label("$6$",(2,0.207106781186548));  label("$5$",(1,-1 - 0.207106781186548));  label("$7$",(3,-1 - 0.207106781186548));  label((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);  /* end of picture */ //Credit to dasobson for the diagram[/asy]