Construction in GCLC language

dim 120 120

point A 80 95
point C 110 40
point E_{b} 50 56.36

color 220 0 0
fontsize 11

cmark_t A
cmark_b C
cmark_r E_{b}
color 0 0 0
fontsize 10


% Constructing a point M_{b} such that AM_{b}/AC=0.5
towards M_{b} A C 0.5 
cmark_rt M_{b}
color 200 200 200
drawsegment A C 
color 0 0 0


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

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 A and H_{b} are not the same
% Constructing bisector m(AH_{b}) of the segment AH_{b}
med m(AH_{b}) A H_{b} 

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

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



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



drawsegment A B
drawsegment A C
drawsegment B C

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