and for 
,
Prove that every natural number occurs exactly once in this sequence.
inscribed in 
,
is the midpoint of arc 
of 
intersects 
at 
.
intersects 
different from 
.
is the orthocenter of triangle 
= 
for which the number![\[x^4 + x^3 + x^2 + x + 1\]](http://latex.artofproblemsolving.com/a/f/f/affe758628a67ad6f72e82decfe71356c24daa6e.png)
?
Y by Adventure10, Mango247
There are some segments on the plane such that no two of them intersect each other (even at the ending points). We say segment 
breaks segment 
if the extension of cuts at some point between 
and 
.
![[asy]
/* Geogebra to Asymptote conversion, documentation at artofproblemsolving.com/Wiki go to User:Azjps/geogebra */
import graph; size(4cm);
real labelscalefactor = 0.5; /* changes label-to-point distance */
pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); /* default pen style */
pen dotstyle = black; /* point style */
real xmin = -5.267474904743955, xmax = 11.572179069738377, ymin = -10.642621257034536, ymax = 4.543526642434019; /* image dimensions */
/* draw figures */
draw((-4,-2)--(1.08,-2.03), linewidth(2));
draw(shift((-2.1866176795507295,-2.0107089507113147))*scale(0.21166666666666667)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw((-0.16981767035094117,3.225314210196242)--(-2.1866176795507295,-2.0107089507113147), linewidth(2) + linetype("4 4"));
draw((-0.16981767035094117,3.225314210196242)--(-0.8194002739586808,1.538865607509914), linewidth(2));
label("$A$",(-1.2684397405642523,3.860690076971137),SE*labelscalefactor,fontsize(16));
label("$B$",(-1.9211395070170559,2.002590777612728),SE*labelscalefactor,fontsize(16));
label("$C$",(-4.971261820527631,-1.6571211388676117),SE*labelscalefactor,fontsize(16));
label("$D$",(1.08925640451367566,-1.6571211388676117),SE*labelscalefactor,fontsize(16));
/* dots and labels */
dot((-4,-2),dotstyle);
dot((1.08,-2.03),dotstyle);
dot((-0.16981767035094117,3.225314210196242),dotstyle);
dot((-0.8194002739586808,1.538865607509914),dotstyle);
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);
/* end of picture */
[/asy]](//latex.artofproblemsolving.com/e/5/1/e51af5403b5c262c5fc3993a7d5304ed62e93119.png)
Is it possible that each segment when extended from both ends, breaks exactly one other segment from each way?
![[asy]
/* Geogebra to Asymptote conversion, documentation at artofproblemsolving.com/Wiki go to User:Azjps/geogebra */
import graph; size(4cm);
real labelscalefactor = 0.5; /* changes label-to-point distance */
pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); /* default pen style */
pen dotstyle = black; /* point style */
real xmin = -6.8, xmax = 8.68, ymin = -10.32, ymax = 3.64; /* image dimensions */
/* draw figures */
draw((-2.56,1.24)--(-0.36,1.4), linewidth(2));
draw((-3.32,-2.68)--(-1.24,-3.08), linewidth(2));
draw(shift((-2.551651190956802,-2.8277593863544612))*scale(0.17638888888888887)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw(shift((-0.8889576602618603,1.3615303519809556))*scale(0.17638888888888887)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw((-2.551651190956802,-2.8277593863544612)--(-0.8889576602618603,1.3615303519809556), linewidth(2) + linetype("4 4"));
draw((-1.4097008194020806,0.049476186483185636)--(-1.8514772275312024,-1.0636149148218605), linewidth(2));
/* dots and labels */
dot((-2.56,1.24),dotstyle);
dot((-0.36,1.4),dotstyle);
dot((-3.32,-2.68),dotstyle);
dot((-1.24,-3.08),dotstyle);
dot((-1.4097008194020806,0.049476186483185636),dotstyle);
dot((-1.8514772275312024,-1.0636149148218605),dotstyle);
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);
/* end of picture */
[/asy]](//latex.artofproblemsolving.com/f/a/2/fa24cfd77dcf88ae59cabadbeaac7e6ef962fb05.png)
A segment is called surrounded if from both sides of it, there is exactly one segment that breaks it.
(e.g. segment in the figure.) Is it possible to have all segments to be surrounded?
![[asy]
/* 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(10); defaultpen(dps); /* default pen style */
pen dotstyle = black; /* point style */
real xmin = -10.70976151557872, xmax = 18.64292748469251, ymin = -16.354300717041443, ymax = 9.136192362141452; /* image dimensions */
/* draw figures */
draw((1.0313140845297686,0.748205038977829)--(-1.3,-4), linewidth(2.8));
draw((-5.780195085389632,-2.13088646583346)--(-2.549994860479401,-2.13088646583346), linewidth(2.8));
draw((4.121070821400425,-3.816208322308361)--(1.78,-1.88), linewidth(2.8));
draw(shift((-0.38228674372374466,-2.13088646583346))*scale(0.21166666666666667)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw((-2.549994860479401,-2.13088646583346)--(-0.38228674372374466,-2.13088646583346), linewidth(2.8) + linetype("4 4"));
draw(shift((0.32979226045261084,-0.6805897691262632))*scale(0.21166666666666667)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw((4.121070821400425,-3.816208322308361)--(0.32979226045261084,-0.6805897691262632), linewidth(2.8) + linetype("4 4"));
draw((-3.6313140845297687,-8.74820503897783)--(3.600422205681574,5.980726991931396), linewidth(2.8) + linetype("2 2"));
label("$A$",(-0.397698406272906,1.754593418658662),SE*labelscalefactor,fontsize(16));
label("$B$",(-2.6377720405041316,-3.266261278756151),SE*labelscalefactor,fontsize(16));
/* dots and labels */
dot((1.0313140845297686,0.748205038977829),linewidth(6pt) + dotstyle);
dot((-1.3,-4),linewidth(6pt) + dotstyle);
dot((-5.780195085389632,-2.13088646583346),linewidth(6pt) + dotstyle);
dot((-2.549994860479401,-2.13088646583346),linewidth(6pt) + dotstyle);
dot((4.121070821400425,-3.816208322308361),linewidth(6pt) + dotstyle);
dot((1.78,-1.88),linewidth(6pt) + dotstyle);
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);
/* end of picture */
[/asy]](//latex.artofproblemsolving.com/c/2/2/c2221122d01f43745f44f5c9f4fe907ef7dd93ed.png)
Proposed by Morteza Saghafian
breaks segment 
if the extension of cuts at some point between 
and 
.![[asy]
/* Geogebra to Asymptote conversion, documentation at artofproblemsolving.com/Wiki go to User:Azjps/geogebra */
import graph; size(4cm);
real labelscalefactor = 0.5; /* changes label-to-point distance */
pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); /* default pen style */
pen dotstyle = black; /* point style */
real xmin = -5.267474904743955, xmax = 11.572179069738377, ymin = -10.642621257034536, ymax = 4.543526642434019; /* image dimensions */
/* draw figures */
draw((-4,-2)--(1.08,-2.03), linewidth(2));
draw(shift((-2.1866176795507295,-2.0107089507113147))*scale(0.21166666666666667)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw((-0.16981767035094117,3.225314210196242)--(-2.1866176795507295,-2.0107089507113147), linewidth(2) + linetype("4 4"));
draw((-0.16981767035094117,3.225314210196242)--(-0.8194002739586808,1.538865607509914), linewidth(2));
label("$A$",(-1.2684397405642523,3.860690076971137),SE*labelscalefactor,fontsize(16));
label("$B$",(-1.9211395070170559,2.002590777612728),SE*labelscalefactor,fontsize(16));
label("$C$",(-4.971261820527631,-1.6571211388676117),SE*labelscalefactor,fontsize(16));
label("$D$",(1.08925640451367566,-1.6571211388676117),SE*labelscalefactor,fontsize(16));
/* dots and labels */
dot((-4,-2),dotstyle);
dot((1.08,-2.03),dotstyle);
dot((-0.16981767035094117,3.225314210196242),dotstyle);
dot((-0.8194002739586808,1.538865607509914),dotstyle);
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);
/* end of picture */
[/asy]](http://latex.artofproblemsolving.com/e/5/1/e51af5403b5c262c5fc3993a7d5304ed62e93119.png)
Is it possible that each segment when extended from both ends, breaks exactly one other segment from each way?![[asy]
/* Geogebra to Asymptote conversion, documentation at artofproblemsolving.com/Wiki go to User:Azjps/geogebra */
import graph; size(4cm);
real labelscalefactor = 0.5; /* changes label-to-point distance */
pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); /* default pen style */
pen dotstyle = black; /* point style */
real xmin = -6.8, xmax = 8.68, ymin = -10.32, ymax = 3.64; /* image dimensions */
/* draw figures */
draw((-2.56,1.24)--(-0.36,1.4), linewidth(2));
draw((-3.32,-2.68)--(-1.24,-3.08), linewidth(2));
draw(shift((-2.551651190956802,-2.8277593863544612))*scale(0.17638888888888887)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw(shift((-0.8889576602618603,1.3615303519809556))*scale(0.17638888888888887)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw((-2.551651190956802,-2.8277593863544612)--(-0.8889576602618603,1.3615303519809556), linewidth(2) + linetype("4 4"));
draw((-1.4097008194020806,0.049476186483185636)--(-1.8514772275312024,-1.0636149148218605), linewidth(2));
/* dots and labels */
dot((-2.56,1.24),dotstyle);
dot((-0.36,1.4),dotstyle);
dot((-3.32,-2.68),dotstyle);
dot((-1.24,-3.08),dotstyle);
dot((-1.4097008194020806,0.049476186483185636),dotstyle);
dot((-1.8514772275312024,-1.0636149148218605),dotstyle);
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);
/* end of picture */
[/asy]](http://latex.artofproblemsolving.com/f/a/2/fa24cfd77dcf88ae59cabadbeaac7e6ef962fb05.png)
A segment is called surrounded if from both sides of it, there is exactly one segment that breaks it.(e.g. segment
in the figure.) Is it possible to have all segments to be surrounded?![[asy]
/* 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(10); defaultpen(dps); /* default pen style */
pen dotstyle = black; /* point style */
real xmin = -10.70976151557872, xmax = 18.64292748469251, ymin = -16.354300717041443, ymax = 9.136192362141452; /* image dimensions */
/* draw figures */
draw((1.0313140845297686,0.748205038977829)--(-1.3,-4), linewidth(2.8));
draw((-5.780195085389632,-2.13088646583346)--(-2.549994860479401,-2.13088646583346), linewidth(2.8));
draw((4.121070821400425,-3.816208322308361)--(1.78,-1.88), linewidth(2.8));
draw(shift((-0.38228674372374466,-2.13088646583346))*scale(0.21166666666666667)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw((-2.549994860479401,-2.13088646583346)--(-0.38228674372374466,-2.13088646583346), linewidth(2.8) + linetype("4 4"));
draw(shift((0.32979226045261084,-0.6805897691262632))*scale(0.21166666666666667)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw((4.121070821400425,-3.816208322308361)--(0.32979226045261084,-0.6805897691262632), linewidth(2.8) + linetype("4 4"));
draw((-3.6313140845297687,-8.74820503897783)--(3.600422205681574,5.980726991931396), linewidth(2.8) + linetype("2 2"));
label("$A$",(-0.397698406272906,1.754593418658662),SE*labelscalefactor,fontsize(16));
label("$B$",(-2.6377720405041316,-3.266261278756151),SE*labelscalefactor,fontsize(16));
/* dots and labels */
dot((1.0313140845297686,0.748205038977829),linewidth(6pt) + dotstyle);
dot((-1.3,-4),linewidth(6pt) + dotstyle);
dot((-5.780195085389632,-2.13088646583346),linewidth(6pt) + dotstyle);
dot((-2.549994860479401,-2.13088646583346),linewidth(6pt) + dotstyle);
dot((4.121070821400425,-3.816208322308361),linewidth(6pt) + dotstyle);
dot((1.78,-1.88),linewidth(6pt) + dotstyle);
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);
/* end of picture */
[/asy]](http://latex.artofproblemsolving.com/c/2/2/c2221122d01f43745f44f5c9f4fe907ef7dd93ed.png)
Proposed by Morteza Saghafian
This post has been edited 1 time. Last edited by bgn, Sep 20, 2018, 7:38 AM
be the segments. Take a circle such that cover all the vertices 
and 
.
,![[asy]
/* Geogebra to Asymptote conversion, documentation at artofproblemsolving.com/Wiki go to User:Azjps/geogebra */
import graph; size(10cm);
real labelscalefactor = 0.5; /* changes label-to-point distance */
pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); /* default pen style */
pen dotstyle = black; /* point style */
real xmin = -14.025072561607061, xmax = 14.704173025957557, ymin = -8.044830303919722, ymax = 9.192717048619048; /* image dimensions */
pen ffqqff = rgb(1,0,1);
/* draw figures */
draw(circle((-3.05,-0.74), 5.685384771499638), linewidth(1.2) + ffqqff);
draw((-4.49,4.76)--(-2.87,4.26), linewidth(2));
draw((-6.89,-0.42)--(-5.01,-2.82), linewidth(2));
draw((-0.35,0.18)--(-1.67,-1.54), linewidth(2));
draw((1.31,-2.34)--(-0.41,-1.38), linewidth(2));
draw((0.37,0)--(0.25,1.66), linewidth(2));
draw((1.11,-3.38)--(1.85,-2.08), linewidth(2));
draw((-5.17,2)--(-5.87,0.46), linewidth(2));
draw((-3.91,-5.04)--(-1.35,-3.88), linewidth(2));
draw((-5.17,-4.14)--(-6.83,-3.3), linewidth(2));
/* dots and labels */
dot((-4.49,4.76),dotstyle);
label("$A_1$", (-4.801472662441576,5.236145507173746), NE * labelscalefactor);
dot((-2.87,4.26),dotstyle);
label("$B_1$", (-2.659379789684565,4.480112728553625), NE * labelscalefactor);
dot((-6.89,-0.42),dotstyle);
dot((-5.01,-2.82),dotstyle);
dot((-0.35,0.18),dotstyle);
dot((-1.67,-1.54),dotstyle);
dot((1.31,-2.34),dotstyle);
dot((-0.41,-1.38),dotstyle);
dot((0.37,0),dotstyle);
dot((0.25,1.66),dotstyle);
dot((1.11,-3.38),dotstyle);
dot((1.85,-2.08),dotstyle);
dot((-5.17,2),dotstyle);
dot((-5.87,0.46),dotstyle);
dot((-3.59,-0.88),linewidth(2pt) + dotstyle);
dot((-3.07,-0.88),linewidth(2pt) + dotstyle);
dot((-2.55,-0.88),linewidth(2pt) + dotstyle);
dot((-3.91,-5.04),dotstyle);
dot((-1.35,-3.88),dotstyle);
dot((-5.17,-4.14),dotstyle);
dot((-6.83,-3.3),dotstyle);
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);
/* end of picture */
[/asy]](http://latex.artofproblemsolving.com/8/2/3/823e44d35b4d69f4f40c989d912a88de4bf3cd33.png)
breaks some segment, say 
,![[asy]
/* Geogebra to Asymptote conversion, documentation at artofproblemsolving.com/Wiki go to User:Azjps/geogebra */
import graph; size(15cm);
real labelscalefactor = 0.5; /* changes label-to-point distance */
pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); /* default pen style */
pen dotstyle = black; /* point style */
real xmin = -20.426545367053137, xmax = 15.026100359159813, ymin = -11.779964645572868, ymax = 10.535026362031354; /* image dimensions */
/* draw figures */
draw((xmin, 0.00031524385866197176*xmin-3.464477802991963)--(xmax, 0.00031524385866197176*xmax-3.464477802991963), linewidth(1.2) + linetype("4 4") + gray); /* line */
draw((xmin, -1.7307905202742555*xmin-14.960334143085408)--(xmax, -1.7307905202742555*xmax-14.960334143085408), linewidth(1.2) + linetype("4 4") + gray); /* line */
draw((xmin, 1.7333124718954385*xmin + 14.512866609049581)--(xmax, 1.7333124718954385*xmax + 14.512866609049581), linewidth(1.2) + linetype("4 4") + gray); /* line */
draw((xmin, 0.00031524385866197176*xmin + 3.000917359628707)--(xmax, 0.00031524385866197176*xmax + 3.000917359628707), linewidth(1.2) + linetype("4 4") + gray); /* line */
draw((xmin, -1.730790520274257*xmin-2.0366004139980878)--(xmax, -1.730790520274257*xmax-2.0366004139980878), linewidth(1.2) + linetype("4 4") + gray); /* line */
draw((xmin, 1.7333124718954354*xmin + 1.5750119773818703)--(xmax, 1.7333124718954354*xmax + 1.5750119773818703), linewidth(1.2) + linetype("4 4") + gray); /* line */
draw((-6.188145502801059,2.998966584762442)--(-3.364651763794784,2.999856673823634), linewidth(2));
draw((-2.6825499939928483,2.6063316857664987)--(-1.2700322847510856,0.1615594248913467), linewidth(2));
draw((-1.2697840365315651,-0.6259205297520207)--(-2.6807600662960818,-3.0715828796883624), linewidth(2));
draw((-3.3626135878784957,-3.4655378462745947)--(-6.186107326884771,-3.466427935335787), linewidth(2));
draw((-6.868209096686704,-3.0729029472786533)--(-8.280726805928468,-0.6281306864035008), linewidth(2));
draw((-8.280975054147987,0.1593492682398702)--(-6.869999024383477,2.605011618176204), linewidth(2));
draw((xmin, -0.5769300205325729*xmin-2.9883454498997817)--(xmax, -0.5769300205325729*xmax-2.9883454498997817), linewidth(1.2) + linetype("4 4") + gray); /* line */
draw((xmin, 0.5777706708501866*xmin + 2.525788612719145)--(xmax, 0.5777706708501866*xmax + 2.525788612719145), linewidth(1.2) + linetype("4 4") + gray); /* line */
draw((-4.776873172022336, -3172.147442441616*xmin-15148.441297068335)--(-4.776873172022336, -3172.147442441616*xmax-15148.441297068335), linewidth(1.2) + linetype("4 4") + gray); /* line */
draw(shift((-10.375594533191688,2.997646517172149))*scale(0.17638888888888887)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw((-8.879358238777593,2.1344228811142454)--(-11.871830827605788,3.860870153230057), linewidth(2));
draw((-4.776873172022336,4.504718430286301)--(-4.777962270489793,7.959499348398009), linewidth(2));
draw((-0.672894478584521,2.1370099184159796)--(2.318489011776215,3.8653435644118748), linewidth(2));
draw((2.3210717369262346,-4.327441414742209)--(-0.6714008519019602,-2.600994142626397), linewidth(2));
draw((-4.773885918657218,-4.9712896917984555)--(-4.77279682018976,-8.426070609910163), linewidth(2));
draw((-11.86924810245577,-4.331914825924029)--(-8.877864612095033,-2.603581179928134), linewidth(2));
draw(shift((-4.777417721256066,6.232108889342155))*scale(0.17638888888888887)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw(shift((0.822797266595847,3.001176741413925))*scale(0.17638888888888887)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw(shift((0.8248354425121301,-3.4642177786843042))*scale(0.17638888888888887)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw(shift((-4.773341369423489,-6.6986801508543))*scale(0.17638888888888887)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw(shift((-10.373556357275397,-3.46774800292608))*scale(0.17638888888888887)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw(shift((-4.774360457381632,-3.465982890805191))*scale(0.17638888888888887)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw(shift((-1.9762911393719675,1.3839455553289235))*scale(0.17638888888888887)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw(shift((-4.77639863329792,2.999411629293039))*scale(0.17638888888888887)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw(shift((-7.575487039265734,1.3821804432080378))*scale(0.17638888888888887)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
draw(shift((-7.574467951307587,-1.8505168168410775))*scale(0.17638888888888887)*(expi(pi/4)--expi(5*pi/4)^^expi(3*pi/4)--expi(7*pi/4))); /* special point */
/* dots and labels */
dot((-6.186107326884771,-3.466427935335787),linewidth(6pt) + dotstyle);
dot((-3.3626135878784957,-3.4655378462745947),linewidth(6pt) + dotstyle);
dot((-2.6807600662960818,-3.0715828796883624),linewidth(6pt) + dotstyle);
dot((-1.2697840365315651,-0.6259205297520207),linewidth(6pt) + dotstyle);
dot((-1.2700322847510856,0.1615594248913467),linewidth(6pt) + dotstyle);
dot((-2.6825499939928483,2.6063316857664987),linewidth(6pt) + dotstyle);
dot((-3.364651763794784,2.999856673823634),linewidth(6pt) + dotstyle);
dot((-6.188145502801059,2.998966584762442),linewidth(6pt) + dotstyle);
dot((-6.869999024383477,2.605011618176204),linewidth(6pt) + dotstyle);
dot((-8.280975054147987,0.1593492682398702),linewidth(6pt) + dotstyle);
dot((-8.280726805928468,-0.6281306864035008),linewidth(6pt) + dotstyle);
dot((-6.868209096686704,-3.0729029472786533),linewidth(6pt) + dotstyle);
dot((-8.879358238777593,2.1344228811142454),dotstyle);
dot((-11.871830827605788,3.860870153230057),dotstyle);
dot((-4.776873172022336,4.504718430286301),dotstyle);
dot((-4.777962270489793,7.959499348398009),dotstyle);
dot((2.318489011776215,3.8653435644118748),dotstyle);
dot((-0.672894478584521,2.1370099184159796),dotstyle);
dot((2.3210717369262346,-4.327441414742209),dotstyle);
dot((-0.6714008519019602,-2.600994142626397),dotstyle);
dot((-4.773885918657218,-4.9712896917984555),dotstyle);
dot((-4.77279682018976,-8.426070609910163),dotstyle);
dot((-11.86924810245577,-4.331914825924029),dotstyle);
dot((-8.877864612095033,-2.603581179928134),dotstyle);
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);
/* end of picture */
[/asy]](http://latex.artofproblemsolving.com/5/2/8/52869014d008ccff1ecc66eb5664d94d3aca9e47.png)
