Construction in GCLC language

dim 120 120

point M_{b} 95 67.5
point T_{b} 94.25 68.88

color 220 0 0
fontsize 11

cmark_rt M_{b}
cmark_rt T_{b}
color 0 0 0
fontsize 10


% point O is given by the problem setting, but it has to belong to the line m_{b} which is constructible from the others objects given 
% DET:  points M_{b} and T_{b} are not the same
% Constructing a line b which passes through point M_{b} and point T_{b}
line b M_{b} T_{b} 

color 200 200 200
drawline b
color 0 0 0




% Constructing a line m_{b} which is perpendicular to line b and which passes through point M_{b}
perp m_{b} M_{b} b 

color 200 200 200
drawline m_{b}
color 0 0 0




% Constructing a point P_{\_G51779} with coordinates (10,30)
point P_{\_G51779} 10 30 
cmark_r P_{\_G51779}

% Constructing a line L_{\_G51782} which passes through point T_{b} and point M_{b}
line L_{\_G51782} T_{b} M_{b} 

color 200 200 200
drawline L_{\_G51782}
color 0 0 0


% Constructing a line L_{\_G51785} which is perpendicular to line L_{\_G51782} and which passes through point M_{b}
perp L_{\_G51785} M_{b} L_{\_G51782} 

color 200 200 200
drawline L_{\_G51785}
color 0 0 0


% Constructing a line L_{\_G51788} which passes through point T_{b} and point P_{\_G51779}
line L_{\_G51788} T_{b} P_{\_G51779} 

color 200 200 200
drawline L_{\_G51788}
color 0 0 0


% Constructing a point O which belongs to line L_{\_G51788} and line L_{\_G51785}
intersec O L_{\_G51788} L_{\_G51785} 
color 220 0 0
fontsize 11
cmark_t O
color 0 0 0
fontsize 10




% Constructing a point A such that M_{b}A/M_{b}T_{b}=0.8015166344209094
towards A M_{b} T_{b} 0.8015166344209094 
cmark_t A
color 200 200 200
drawsegment M_{b} T_{b} 
color 0 0 0



% Constructing a point C such that AC/AM_{b}=2
towards C A M_{b} 2 
cmark_b C
color 200 200 200
drawsegment A C 
color 0 0 0


% NDG:  points A and O are not the same
% Constructing a circle k(O,C) whose center is at point O and which passes through point A
circle k(O,C) O A 

color 200 200 200
drawcircle k(O,C)
color 0 0 0



% NDG:  line m_{b} and circle k(O,C) intersect
% Constructing points N_{b} and N_{bk} which are in intersection of k(O,C) and m_{b}
intersec2 N_{b} N_{bk} k(O,C) m_{b} 
cmark_rb N_{b}
cmark_r N_{bk}


% DET:  points N_{b} and T_{b} are not the same
% Constructing a line s_{b} which passes through point N_{b} and point T_{b}
line s_{b} N_{b} T_{b} 

color 200 200 200
drawline s_{b}
color 0 0 0



% NDG:  line s_{b} and circle k(O,C) intersect% DET:  points N_{b} and B must be different
% Constructing a point P_{\_G52443} which is a foot of the point O on the line s_{b}
foot P_{\_G52443} O s_{b} 
cmark_r P_{\_G52443}
color 200 200 200
drawline O P_{\_G52443} 
color 0 0 0

% Constructing a point B which is an image of the point N_{b} in the symmetry to point/line P_{\_G52443}
sim B P_{\_G52443} N_{b} 
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  line s_{b} and circle k(O,C) intersect; line m_{b} and circle k(O,C) intersect; points A and O are not the same
% Determination conditions:  points N_{b} and B must be different; points N_{b} and T_{b} are not the same; points M_{b} and T_{b} are not the same