User:Infdef

[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 = -3.792592592592592, xmax = 3.792592592592592, ymin = -1.8883950617283929, ymax = 1.8883950617283933; /* image dimensions */ pen cqcqcq = rgb(0.7529411764705882,0.7529411764705882,0.7529411764705882);

/* draw figures *//* special point */

draw(circle((0,0), 1), linewidth(1)); draw((-1,0)--(1,0), linewidth(1)); draw((0,0)--(0,1), linewidth(1)); draw((0,0.25)--(1,0), linewidth(1)); draw((0,0.25)--(0.08603768285222771,0), linewidth(1)); draw((0,0.25)--(-0.12198209123162133,0), linewidth(1)); draw(shift((0.43900895438418935,0))*xscale(0.5609910456158107)*yscale(0.5609910456158107)*arc((0,0),1,0,180), linewidth(1)); draw(shift((0.08603768285222771,0))*xscale(0.3597006729243106)*yscale(0.3597006729243106)*arc((0,0),1,0,180), linewidth(1)); label("",(-0.9616049382716048,-0.040308641975308805),SE*labelscalefactor); label("",(-0.05,1.13),SE*labelscalefactor); label("",(0.8646913580246911,-0.035530864197530880),SE*labelscalefactor); label("",(0.04345679012345678,-0.03555555555555574),SE*labelscalefactor); label("",(-0.1698765432098765,-0.03555555555555574),SE*labelscalefactor); label("",(-0.051358024691358015,-0.03950617283950635),SE*labelscalefactor); label("",(0.03160493827160493,0.3432098765432097),SE*labelscalefactor); label("",(-0.11456790123456788,0.5096296296296293),SE*labelscalefactor); label("",(-0.3595061728395061,-0.03555555555555574),SE*labelscalefactor); label("",(0.3516049382716049,-0.031604938271605126),SE*labelscalefactor); /* special point */ label("",(-0.2686419753086419,1.1317283950617274),SE*labelscalefactor); draw((-0.2736629900720829,0)--(-0.2736629900720829,0.9618256431728192), linewidth(2)); /* special point */ label("",(0.34765432098765425,1.0503703703703693),SE*labelscalefactor); draw((0.4457383557765383,0)--(0.4457383557765383,0.8951632913550622), linewidth(2)); draw((-0.2736629900720829,0.9618256431728192)--(0.4457383557765383,0.8951632913550622), linewidth(1)); label("",(0.09876543209876541,0.8718518518518511),SE*labelscalefactor); /* special point */ draw((0,0)--(0.092268359463302,0.9957341762950346), linewidth(1)); label("",(0.10271604938271603,1.1417283950617274),SE*labelscalefactor); draw(circle((-0.2736629900720829,0.9618256431728192), 0.3674990356331406), linewidth(1) + linetype("2 2") + cqcqcq); /* special point */ draw(circle((-0.6026346363792564,0.7980172272802395), 0.3674990356331407), linewidth(1) + linetype("2 2") + cqcqcq); /* special point */ draw(circle((-0.8502171357296141,0.5264321628773558), 0.36749903563314057), linewidth(1) + linetype("2 2") + cqcqcq); /* special point */ draw(circle((-0.9829730996839017,0.18374951781657067), 0.36749903563314035), linewidth(1) + linetype("2 2") + cqcqcq); /* special point */ draw(circle((-0.9829730996839019,-0.1837495178165696), 0.36749903563314024), linewidth(1) + linetype("2 2") + cqcqcq); /* special point */ draw(circle((-0.8502171357296147,-0.526432162877355), 0.36749903563314046), linewidth(1) + linetype("2 2") + cqcqcq); /* special point */ draw(circle((-0.6026346363792574,-0.7980172272802387), 0.36749903563314035), linewidth(1) + linetype("2 2") + cqcqcq); /* special point */ draw(circle((-0.2736629900720844,-0.9618256431728187), 0.3674990356331404), linewidth(1) + linetype("2 2") + cqcqcq); /* special point */ draw(circle((0.09226835946330011,-0.9957341762950347), 0.3674990356331404), linewidth(1) + linetype("2 2") + cqcqcq); /* special point */ draw(circle((0.44573835577653625,-0.8951632913550633), 0.36749903563314035), linewidth(1) + linetype("2 2") + cqcqcq); /* special point */ draw(circle((0.7390089172206573,-0.6736956436465591), 0.36749903563314035), linewidth(1) + linetype("2 2") + cqcqcq); /* special point */ draw(circle((0.9324722294043546,-0.36124166618715586), 0.3674990356331401), linewidth(1) + linetype("2 2") + cqcqcq); draw(circle((1,0), 0.36749903563314373), linewidth(1) + linetype("2 2") + cqcqcq); /* special point */ draw(circle((0.9324722294043547,0.36124166618715575), 0.3674990356331436), linewidth(1) + linetype("2 2") + cqcqcq); /* special point */ draw(circle((0.7390089172206551,0.6736956436465616), 0.3674990356331436), linewidth(1) + linetype("2 2") + cqcqcq); draw(circle((0.4457383557765383,0.8951632913550622), 0.36749903563313474), linewidth(1) + linetype("2 2") + cqcqcq); draw(circle((0.092268359463302,0.9957341762950346), 0.36749903563314074), linewidth(1) + linetype("2 2") + cqcqcq); draw((0.092268359463302,0.9957341762950346)--(0.4457383557765383,0.8951632913550622), linewidth(1) + red); draw((0.4457383557765383,0.8951632913550622)--(0.7390089172206551,0.6736956436465616), linewidth(1) + red); draw((0.7390089172206551,0.6736956436465616)--(0.9324722294043547,0.36124166618715575), linewidth(1) + red); draw((0.9324722294043547,0.36124166618715575)--(1,0), linewidth(1) + red); draw((1,0)--(0.9324722294043546,-0.36124166618715586), linewidth(1) + red); draw((0.9324722294043546,-0.36124166618715586)--(0.7390089172206573,-0.6736956436465591), linewidth(1) + red); draw((0.7390089172206573,-0.6736956436465591)--(0.44573835577653625,-0.8951632913550633), linewidth(1) + red); draw((0.44573835577653625,-0.8951632913550633)--(0.09226835946330011,-0.9957341762950347), linewidth(1) + red); draw((0.09226835946330011,-0.9957341762950347)--(-0.2736629900720844,-0.9618256431728187), linewidth(1) + red); draw((-0.2736629900720844,-0.9618256431728187)--(-0.6026346363792574,-0.7980172272802387), linewidth(1) + red); draw((-0.6026346363792574,-0.7980172272802387)--(-0.8502171357296147,-0.526432162877355), linewidth(1) + red); draw((-0.8502171357296147,-0.526432162877355)--(-0.9829730996839019,-0.1837495178165696), linewidth(1) + red); draw((-0.9829730996839019,-0.1837495178165696)--(-0.9829730996839017,0.18374951781657067), linewidth(1) + red); draw((-0.9829730996839017,0.18374951781657067)--(-0.8502171357296141,0.5264321628773558), linewidth(1)+ red); draw((-0.8502171357296141,0.5264321628773558)--(-0.6026346363792564,0.7980172272802395), linewidth(1) + red); draw((-0.6026346363792564,0.7980172272802395)--(-0.2736629900720829,0.9618256431728192), linewidth(1) + red); draw((-0.2736629900720829,0.9618256431728192)--(0.092268359463302,0.9957341762950346), linewidth(1) + red);

/* dots and labels */

dot((0,0),dotstyle); dot((-1,0),dotstyle); dot((0,1),dotstyle); dot((0,0.25),dotstyle); dot((0.08603768285222771,0),dotstyle); dot((-0.12198209123162133,0),dotstyle); dot((0,0.34925934666322295),dotstyle); dot((-0.2736629900720829,0),dotstyle); dot((0.4457383557765383,0),dotstyle); dot((0.08603768285222771,0.9284944672639407),dotstyle); clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);

/* end of picture */

[/asy]