Construction in GCLC language

dim 120 120

point A 80 95
point E_{c} 95 56.36
point H_{a} 80 40

color 220 0 0
fontsize 11

cmark_t A
cmark_r E_{c}
cmark_b H_{a}
color 0 0 0
fontsize 10

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

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



% NDG:  points H_{a} 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_{a}
circle k(E_{c},C) E_{c} H_{a} 

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



% NDG:  line h_{a} and circle k(E_{c},C) intersect% DET:  points H_{a} and H must be different
% Constructing a point P_{\_G6321} which is a foot of the point E_{c} on the line h_{a}
foot P_{\_G6321} E_{c} h_{a} 
cmark_r P_{\_G6321}
color 200 200 200
drawline E_{c} P_{\_G6321} 
color 0 0 0

% Constructing a point H which is an image of the point H_{a} in the symmetry to point/line P_{\_G6321}
sim H P_{\_G6321} H_{a} 
cmark_rt H



% Constructing a point C such that E_{c}C/E_{c}H=-1
towards C E_{c} H -1 
cmark_b C
color 200 200 200
drawsegment H 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 H_{a} and C are not the same
% Constructing a line a which passes through point H_{a} and point C
line a H_{a} C 

color 200 200 200
drawline a
color 0 0 0



% NDG:  line b and circle k(E_{c},C) intersect% DET:  points C and H_{b} must be different
% Constructing a point P_{\_G6684} which is a foot of the point E_{c} on the line b
foot P_{\_G6684} E_{c} b 
cmark_r P_{\_G6684}
color 200 200 200
drawline E_{c} P_{\_G6684} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point C in the symmetry to point/line P_{\_G6684}
sim H_{b} P_{\_G6684} C 
cmark_rt H_{b}


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

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



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



drawsegment A B
drawsegment A C
drawsegment B C

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