Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point E_{c} 95 56.36
point H_{c} 68.91 84.83

color 220 0 0
fontsize 11

cmark_r E_{a}
cmark_r E_{c}
cmark_lt H_{c}
color 0 0 0
fontsize 10

% 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 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 h_{c} and circle k(E_{a},A) intersect% DET:  points H_{c} and H must be different
% Constructing a point P_{\_G28104} which is a foot of the point E_{a} on the line h_{c}
foot P_{\_G28104} E_{a} h_{c} 
cmark_r P_{\_G28104}
color 200 200 200
drawline E_{a} P_{\_G28104} 
color 0 0 0

% Constructing a point H which is an image of the point H_{c} in the symmetry to point/line P_{\_G28104}
sim H P_{\_G28104} H_{c} 
cmark_rt H



% Constructing a point A such that HA/HE_{a}=2
towards A H E_{a} 2 
cmark_t A
color 200 200 200
drawsegment H A 
color 0 0 0



% 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 H_{c} and A are not the same
% Constructing a line c which passes through point H_{c} and point A
line c H_{c} A 

color 200 200 200
drawline 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



% NDG:  line b and circle k(E_{a},A) intersect% DET:  points A and H_{b} must be different
% Constructing a point P_{\_G28541} which is a foot of the point E_{a} on the line b
foot P_{\_G28541} E_{a} b 
cmark_r P_{\_G28541}
color 200 200 200
drawline E_{a} P_{\_G28541} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point A in the symmetry to point/line P_{\_G28541}
sim H_{b} P_{\_G28541} A 
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 c and h_{b} are not parallel% DET:  lines c and h_{b} are not the same
% Constructing a point B which belongs to line c and line h_{b}
intersec B c h_{b} 
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

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