Construction in GCLC language

dim 120 120

point B 20 40
point E_{c} 95 56.36
point M_{c} 50 67.5

color 220 0 0
fontsize 11

cmark_b B
cmark_r E_{c}
cmark_lt M_{c}
color 0 0 0
fontsize 10


% Constructing a point A such that BA/BM_{c}=2
towards A B M_{c} 2 
cmark_t A
color 200 200 200
drawsegment B A 
color 0 0 0


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

color 200 200 200
drawline c
color 0 0 0



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

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




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

color 200 200 200
drawline h_{c}
color 0 0 0



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


% DET:  points B and H_{c} are not the same
% Constructing bisector m(BH_{c}) of the segment BH_{c}
med m(BH_{c}) B H_{c} 

color 200 200 200
drawline m(BH_{c})
color 0 0 0

color 200 200 200
drawsegment B H_{c} 
color 0 0 0


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

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

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


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


% NDG:  points E_{c} 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_{c}
circle k(N,M_{a}) N E_{c} 

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



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



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



drawsegment A B
drawsegment A C
drawsegment B C

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