Construction in GCLC language

dim 120 120

point A 80 95
point E_{c} 95 56.36
point M_{c} 50 67.5

color 220 0 0
fontsize 11

cmark_t A
cmark_r E_{c}
cmark_lt M_{c}
color 0 0 0
fontsize 10


% Constructing a point B such that AB/AM_{c}=2
towards B A M_{c} 2 
cmark_b B
color 200 200 200
drawsegment A B 
color 0 0 0


% DET:  points A and M_{c} are not the same
% Constructing a line c which passes through point A and point M_{c}
line c A 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 A and H_{c} are not the same
% Constructing bisector m(AH_{c}) of the segment AH_{c}
med m(AH_{c}) A H_{c} 

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

color 200 200 200
drawsegment A 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(AH_{c}) and circle k(N,M_{a}) intersect
% Constructing points M_{b} and E_{a} which are in intersection of k(N,M_{a}) and m(AH_{c})
intersec2 M_{b} E_{a} k(N,M_{a}) m(AH_{c}) 
cmark_rt M_{b}
cmark_r E_{a}



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



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  line m(AH_{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 A 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 A and M_{c} are not the same