Construction in GCLC language

dim 120 120

point C 110 40
point E_{b} 50 56.36
point H_{c} 68.91 84.83

color 220 0 0
fontsize 11

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

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

color 200 200 200
drawline h_{c}
color 0 0 0



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

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



% NDG:  line h_{c} and circle k(E_{b},B) intersect% DET:  points H_{c} and H must be different
% Constructing a point P_{\_G22968} which is a foot of the point E_{b} on the line h_{c}
foot P_{\_G22968} E_{b} h_{c} 
cmark_r P_{\_G22968}
color 200 200 200
drawline E_{b} P_{\_G22968} 
color 0 0 0

% Constructing a point H which is an image of the point H_{c} in the symmetry to point/line P_{\_G22968}
sim H P_{\_G22968} H_{c} 
cmark_rt H



% Constructing a point B such that E_{b}B/E_{b}H=-1
towards B E_{b} H -1 
cmark_b B
color 200 200 200
drawsegment H B 
color 0 0 0


% DET:  points C and B are not the same
% Constructing a line a which passes through point C and point B
line a C B 

color 200 200 200
drawline a
color 0 0 0



% 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:  line a and circle k(E_{b},B) intersect% DET:  points B and H_{a} must be different
% Constructing a point P_{\_G23331} which is a foot of the point E_{b} on the line a
foot P_{\_G23331} E_{b} a 
cmark_r P_{\_G23331}
color 200 200 200
drawline E_{b} P_{\_G23331} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point B in the symmetry to point/line P_{\_G23331}
sim H_{a} P_{\_G23331} B 
cmark_b H_{a}


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

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



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



drawsegment A B
drawsegment A C
drawsegment B C

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