Construction in GCLC language

dim 120 120

point A 80 95
point B 20 40
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_t A
cmark_b B
cmark_r N
color 0 0 0
fontsize 10


% Constructing a point M_{c} such that AM_{c}/AB=0.5
towards M_{c} A B 0.5 
cmark_lt M_{c}
color 200 200 200
drawsegment A B 
color 0 0 0


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

color 200 200 200
drawline c
color 0 0 0



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

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



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

color 200 200 200
drawcircle k(M_{c},A)
color 0 0 0



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

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



% NDG:  line c and circle k(N,M_{a}) intersect% DET:  points M_{c} and H_{c} must be different
% Constructing a point P_{\_G4947} which is a foot of the point N on the line c
foot P_{\_G4947} N c 
cmark_r P_{\_G4947}
color 200 200 200
drawline N P_{\_G4947} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point M_{c} in the symmetry to point/line P_{\_G4947}
sim H_{c} P_{\_G4947} M_{c} 
cmark_lt H_{c}


% NDG:  line m(H_{a}H_{b}) and circle k(N,M_{a}) intersect% DET:  points M_{c} and E_{c} must be different
% Constructing a point E_{c} which is an image of the point M_{c} in the symmetry to point/line N
sim E_{c} N M_{c} 
cmark_r E_{c}


% DET:  points E_{c} and H_{c} are not the same
% Constructing a line h_{c} which passes through point E_{c} and point H_{c}
line h_{c} E_{c} H_{c} 

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



% NDG:  circles k(M_{c},A) and k(N,M_{a}) intersect% DET:  circles k(M_{c},A) and k(N,M_{a}) are not the same
% Constructing points H_{b} and H_{a} which are in intersection of k(M_{c},A) and k(N,M_{a})
intersec2 H_{b} H_{a} k(M_{c},A) k(N,M_{a}) 
cmark_rt H_{b}
cmark_b H_{a}


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

color 200 200 200
drawline b
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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