Construction in GCLC language

dim 120 120

point E_{b} 50 56.36
point E_{c} 95 56.36
point H_{a} 80 40

color 220 0 0
fontsize 11

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

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

color 200 200 200
drawcircle k(E_{b},B)
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:  circles k(E_{b},B) and k(E_{c},C) intersect% DET:  circles k(E_{b},B) and k(E_{c},C) are not the same; points H_{a} and H must be different
% Constructing a line L_{\_G48885} which passes through point E_{b} and point E_{c}
line L_{\_G48885} E_{b} E_{c} 

color 200 200 200
drawline L_{\_G48885}
color 0 0 0


% Constructing a point H which is an image of the point H_{a} in the symmetry to point/line L_{\_G48885}
sim H L_{\_G48885} H_{a} 
cmark_rt H



% Constructing a point B such that HB/HE_{b}=2
towards B H E_{b} 2 
cmark_b B
color 200 200 200
drawsegment H B 
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_{a} and H are not the same
% Constructing a line h_{a} which passes through point H_{a} and point H
line h_{a} H_{a} H 

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



% NDG:  line h_{c} and circle k(E_{b},B) intersect% DET:  points H and H_{c} must be different
% Constructing a point P_{\_G49302} which is a foot of the point E_{b} on the line h_{c}
foot P_{\_G49302} E_{b} h_{c} 
cmark_r P_{\_G49302}
color 200 200 200
drawline E_{b} P_{\_G49302} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point H in the symmetry to point/line P_{\_G49302}
sim H_{c} P_{\_G49302} H 
cmark_lt H_{c}


% 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:  lines h_{a} and c are not parallel% DET:  lines h_{a} and c are not the same
% Constructing a point A which belongs to line h_{a} and line c
intersec A h_{a} c 
cmark_t A



drawsegment A B
drawsegment A C
drawsegment B C

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