Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point E_{c} 95 56.36
point H_{b} 89.36 77.83

color 220 0 0
fontsize 11

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

% NDG:  points H_{b} 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_{b}
circle k(E_{a},A) E_{a} H_{b} 

color 200 200 200
drawcircle k(E_{a},A)
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:  circles k(E_{a},A) and k(E_{c},C) intersect% DET:  circles k(E_{a},A) and k(E_{c},C) are not the same; points H_{b} and H must be different
% Constructing a line L_{\_G19482} which passes through point E_{a} and point E_{c}
line L_{\_G19482} E_{a} E_{c} 

color 200 200 200
drawline L_{\_G19482}
color 0 0 0


% Constructing a point H which is an image of the point H_{b} in the symmetry to point/line L_{\_G19482}
sim H L_{\_G19482} H_{b} 
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 E_{c} and H are not the same
% Constructing a line h_{c} which passes through point E_{c} and point H
line h_{c} E_{c} H 

color 200 200 200
drawline h_{c}
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_{c} and circle k(E_{a},A) intersect% DET:  points H and H_{c} must be different
% Constructing a point P_{\_G19899} which is a foot of the point E_{a} on the line h_{c}
foot P_{\_G19899} E_{a} h_{c} 
cmark_r P_{\_G19899}
color 200 200 200
drawline E_{a} P_{\_G19899} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point H in the symmetry to point/line P_{\_G19899}
sim H_{c} P_{\_G19899} H 
cmark_lt H_{c}


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

color 200 200 200
drawline c
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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