Construction in GCLC language

dim 120 120

point B 20 40
point E_{c} 95 56.36
point H 80 72.73

color 220 0 0
fontsize 11

cmark_b B
cmark_r E_{c}
cmark_rt H
color 0 0 0
fontsize 10


% Constructing a point E_{b} such that BE_{b}/BH=0.5
towards E_{b} B H 0.5 
cmark_r E_{b}
color 200 200 200
drawsegment B H 
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 B and C are not the same
% Constructing a line a which passes through point B and point C
line a B C 

color 200 200 200
drawline a
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



% NDG:  points B 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 B
circle k(E_{b},B) E_{b} B 

color 200 200 200
drawcircle k(E_{b},B)
color 0 0 0



% NDG:  line a and circle k(E_{b},B) intersect% DET:  points B and H_{a} must be different
% Constructing a point P_{\_G11292} which is a foot of the point E_{b} on the line a
foot P_{\_G11292} E_{b} a 
cmark_r P_{\_G11292}
color 200 200 200
drawline E_{b} P_{\_G11292} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point B in the symmetry to point/line P_{\_G11292}
sim H_{a} P_{\_G11292} B 
cmark_b H_{a}


% 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_{\_G11530} which is a foot of the point E_{b} on the line h_{c}
foot P_{\_G11530} E_{b} h_{c} 
cmark_r P_{\_G11530}
color 200 200 200
drawline E_{b} P_{\_G11530} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point H in the symmetry to point/line P_{\_G11530}
sim H_{c} P_{\_G11530} H 
cmark_lt H_{c}


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

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