Construction in GCLC language

dim 120 120

point C 110 40
point E_{b} 50 56.36
point M_{b} 95 67.5

color 220 0 0
fontsize 11

cmark_b C
cmark_r E_{b}
cmark_rt M_{b}
color 0 0 0
fontsize 10


% Constructing a point A such that CA/CM_{b}=2
towards A C M_{b} 2 
cmark_t A
color 200 200 200
drawsegment C A 
color 0 0 0


% DET:  points C and M_{b} are not the same
% Constructing a line b which passes through point C and point M_{b}
line b C M_{b} 

color 200 200 200
drawline b
color 0 0 0



% DET:  points E_{b} and M_{b} are not the same
% Constructing a line m(H_{a}H_{c}) which passes through point E_{b} and point M_{b}
line m(H_{a}H_{c}) E_{b} M_{b} 

color 200 200 200
drawline m(H_{a}H_{c})
color 0 0 0




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

color 200 200 200
drawline h_{b}
color 0 0 0



% NDG:  lines h_{b} and b are not parallel% DET:  lines h_{b} and b are not the same
% Constructing a point H_{b} which belongs to line h_{b} and line b
intersec H_{b} h_{b} b 
cmark_rt H_{b}


% DET:  points C and H_{b} are not the same
% Constructing bisector m(CH_{b}) of the segment CH_{b}
med m(CH_{b}) C H_{b} 

color 200 200 200
drawline m(CH_{b})
color 0 0 0

color 200 200 200
drawsegment C H_{b} 
color 0 0 0


% DET:  points E_{b} and M_{b} are not the same
% Constructing bisector m(E_{b}M_{b}) of the segment E_{b}M_{b}
med m(E_{b}M_{b}) E_{b} M_{b} 

color 200 200 200
drawline m(E_{b}M_{b})
color 0 0 0

color 200 200 200
drawsegment E_{b} M_{b} 
color 0 0 0


% NDG:  lines m(E_{b}M_{b}) and m(H_{a}H_{c}) are not parallel% DET:  lines m(E_{b}M_{b}) and m(H_{a}H_{c}) are not the same
% Constructing a point N which belongs to line m(E_{b}M_{b}) and line m(H_{a}H_{c})
intersec N m(E_{b}M_{b}) m(H_{a}H_{c}) 
cmark_r N


% NDG:  points E_{b} and N are not the same
% Constructing a circle k(N,M_{a}) whose center is at point N and which passes through point E_{b}
circle k(N,M_{a}) N E_{b} 

color 200 200 200
drawcircle k(N,M_{a})
color 0 0 0



% NDG:  line m(CH_{b}) and circle k(N,M_{a}) intersect
% Constructing points M_{a} and E_{c} which are in intersection of k(N,M_{a}) and m(CH_{b})
intersec2 M_{a} E_{c} k(N,M_{a}) m(CH_{b}) 
cmark_b M_{a}
cmark_r E_{c}



% Constructing a point B such that M_{a}B/M_{a}C=-1
towards B M_{a} C -1 
cmark_b B
color 200 200 200
drawsegment C B 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  line m(CH_{b}) and circle k(N,M_{a}) intersect; points E_{b} and N are not the same; lines m(E_{b}M_{b}) and m(H_{a}H_{c}) are not parallel; lines h_{b} and b are not parallel
% Determination conditions:  lines m(E_{b}M_{b}) and m(H_{a}H_{c}) are not the same; points E_{b} and M_{b} are not the same; points C and H_{b} are not the same; lines h_{b} and b are not the same; points E_{b} and M_{b} are not the same; points C and M_{b} are not the same