Construction in GCLC language

dim 120 120

point E_{c} 95 56.36
point H_{c} 68.91 84.83
point O 65 51.14

color 220 0 0
fontsize 11

cmark_r E_{c}
cmark_lt H_{c}
cmark_t O
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




% Constructing a line c which is perpendicular to line h_{c} and which passes through point H_{c}
perp c H_{c} h_{c} 

color 200 200 200
drawline c
color 0 0 0




% Constructing a line m_{c} which is perpendicular to line c and which passes through point O
perp m_{c} O c 

color 200 200 200
drawline m_{c}
color 0 0 0



% NDG:  lines m_{c} and c are not parallel% DET:  lines m_{c} and c are not the same
% Constructing a point M_{c} which belongs to line m_{c} and line c
intersec M_{c} m_{c} c 
cmark_lt M_{c}


% DET:  points M_{c} and E_{c} are not the same
% Constructing a line m(H_{b}H_{a}) which passes through point M_{c} and point E_{c}
line m(H_{b}H_{a}) M_{c} E_{c} 

color 200 200 200
drawline m(H_{b}H_{a})
color 0 0 0



% DET:  points E_{c} and H_{c} are not the same
% Constructing bisector m(E_{c}H_{c}) of the segment E_{c}H_{c}
med m(E_{c}H_{c}) E_{c} H_{c} 

color 200 200 200
drawline m(E_{c}H_{c})
color 0 0 0

color 200 200 200
drawsegment E_{c} H_{c} 
color 0 0 0


% NDG:  lines m(E_{c}H_{c}) and m(H_{b}H_{a}) are not parallel% DET:  lines m(E_{c}H_{c}) and m(H_{b}H_{a}) are not the same
% Constructing a point N which belongs to line m(E_{c}H_{c}) and line m(H_{b}H_{a})
intersec N m(E_{c}H_{c}) m(H_{b}H_{a}) 
cmark_r N



% Constructing a point H such that OH/ON=2
towards H O N 2 
cmark_rt H
color 200 200 200
drawsegment O 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


% NDG:  points C and O are not the same
% Constructing a circle k(O,C) whose center is at point O and which passes through point C
circle k(O,C) O C 

color 200 200 200
drawcircle k(O,C)
color 0 0 0



% NDG:  line c and circle k(O,C) intersect
% Constructing points A and B which are in intersection of k(O,C) and c
intersec2 A B k(O,C) c 
cmark_t A
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  line c and circle k(O,C) intersect; points C and O are not the same; lines m(E_{c}H_{c}) and m(H_{b}H_{a}) are not parallel; lines m_{c} and c are not parallel
% Determination conditions:  lines m(E_{c}H_{c}) and m(H_{b}H_{a}) are not the same; points E_{c} and H_{c} are not the same; points M_{c} and E_{c} are not the same; lines m_{c} and c are not the same; points E_{c} and H_{c} are not the same