Construction in GCLC language

dim 120 120

point B 20 40
point E_{a} 80 83.86
point H_{c} 68.91 84.83

color 220 0 0
fontsize 11

cmark_b B
cmark_r E_{a}
cmark_lt H_{c}
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 E_{a} are not the same
% Constructing a circle k(E_{a},A) whose center is at point E_{a} and which passes through point H_{c}
circle k(E_{a},A) E_{a} H_{c} 

color 200 200 200
drawcircle k(E_{a},A)
color 0 0 0



% NDG:  line c and circle k(E_{a},A) intersect% DET:  points H_{c} and A must be different
% Constructing a point P_{\_G15038} which is a foot of the point E_{a} on the line c
foot P_{\_G15038} E_{a} c 
cmark_r P_{\_G15038}
color 200 200 200
drawline E_{a} P_{\_G15038} 
color 0 0 0

% Constructing a point A which is an image of the point H_{c} in the symmetry to point/line P_{\_G15038}
sim A P_{\_G15038} H_{c} 
cmark_t A



% Constructing a point H such that E_{a}H/E_{a}A=-1
towards H E_{a} A -1 
cmark_rt H
color 200 200 200
drawsegment A H 
color 0 0 0


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

color 200 200 200
drawline h_{b}
color 0 0 0



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

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



% NDG:  line h_{b} and circle k(E_{a},A) intersect% DET:  points H and H_{b} must be different
% Constructing a point P_{\_G15401} which is a foot of the point E_{a} on the line h_{b}
foot P_{\_G15401} E_{a} h_{b} 
cmark_r P_{\_G15401}
color 200 200 200
drawline E_{a} P_{\_G15401} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point H in the symmetry to point/line P_{\_G15401}
sim H_{b} P_{\_G15401} H 
cmark_rt H_{b}


% 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; line h_{b} and circle k(E_{a},A) intersect; line c and circle k(E_{a},A) intersect; points H_{c} and E_{a} are not the same
% Determination conditions:  lines h_{c} and b are not the same; points A and H_{b} are not the same; points H and H_{b} must be different; points H_{c} and H are not the same; points B and H are not the same; points H_{c} and A must be different; points B and H_{c} are not the same