Construction in GCLC language

dim 120 120

point B 20 40
point E_{a} 80 83.86
point M_{a} 65 40

color 220 0 0
fontsize 11

cmark_b B
cmark_r E_{a}
cmark_b M_{a}
color 0 0 0
fontsize 10


% Constructing a point C such that BC/BM_{a}=2
towards C B M_{a} 2 
cmark_b C
color 200 200 200
drawsegment B C 
color 0 0 0


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

color 200 200 200
drawline a
color 0 0 0



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

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




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

color 200 200 200
drawline h_{a}
color 0 0 0



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


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

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

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


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

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

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


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


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

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



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



% Constructing a point A such that M_{c}A/M_{c}B=-1
towards A M_{c} B -1 
cmark_t A
color 200 200 200
drawsegment B A 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

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