Construction in GCLC language

dim 120 120

point A 80 95
point E_{c} 95 56.36
point H_{b} 89.36 77.83

color 220 0 0
fontsize 11

cmark_t A
cmark_r E_{c}
cmark_rt H_{b}
color 0 0 0
fontsize 10

% 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:  points H_{b} and E_{c} are not the same
% Constructing a circle k(E_{c},C) whose center is at point E_{c} and which passes through point H_{b}
circle k(E_{c},C) E_{c} H_{b} 

color 200 200 200
drawcircle k(E_{c},C)
color 0 0 0



% NDG:  line b and circle k(E_{c},C) intersect% DET:  points H_{b} and C must be different
% Constructing a point P_{\_G15069} which is a foot of the point E_{c} on the line b
foot P_{\_G15069} E_{c} b 
cmark_r P_{\_G15069}
color 200 200 200
drawline E_{c} P_{\_G15069} 
color 0 0 0

% Constructing a point C which is an image of the point H_{b} in the symmetry to point/line P_{\_G15069}
sim C P_{\_G15069} H_{b} 
cmark_b C



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


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

color 200 200 200
drawline h_{a}
color 0 0 0



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

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



% NDG:  line h_{a} and circle k(E_{c},C) intersect% DET:  points H and H_{a} must be different
% Constructing a point P_{\_G15432} which is a foot of the point E_{c} on the line h_{a}
foot P_{\_G15432} E_{c} h_{a} 
cmark_r P_{\_G15432}
color 200 200 200
drawline E_{c} P_{\_G15432} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point H in the symmetry to point/line P_{\_G15432}
sim H_{a} P_{\_G15432} H 
cmark_b H_{a}


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

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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