Construction in GCLC language

dim 120 120

point B 20 40
point H_{c} 68.91 84.83
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_b B
cmark_lt H_{c}
cmark_r N
color 0 0 0
fontsize 10

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

color 200 200 200
drawline c
color 0 0 0



% NDG:  points H_{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 H_{c}
circle k(N,M_{a}) N H_{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 H_{c} and M_{c} must be different
% Constructing a point P_{\_G31651} which is a foot of the point N on the line c
foot P_{\_G31651} N c 
cmark_r P_{\_G31651}
color 200 200 200
drawline N P_{\_G31651} 
color 0 0 0

% Constructing a point M_{c} which is an image of the point H_{c} in the symmetry to point/line P_{\_G31651}
sim M_{c} P_{\_G31651} H_{c} 
cmark_lt M_{c}



% 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


% 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:  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:  points B 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 B
circle k(M_{c},A) M_{c} B 

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



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


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

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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