Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point H_{a} 80 40
point O 65 51.14

color 220 0 0
fontsize 11

cmark_r E_{a}
cmark_b H_{a}
cmark_t O
color 0 0 0
fontsize 10

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

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




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

color 200 200 200
drawline a
color 0 0 0




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

color 200 200 200
drawline m_{a}
color 0 0 0



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


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

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



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

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

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


% NDG:  lines m(E_{a}H_{a}) and m(H_{b}H_{c}) are not parallel% DET:  lines m(E_{a}H_{a}) and m(H_{b}H_{c}) are not the same
% Constructing a point N which belongs to line m(E_{a}H_{a}) and line m(H_{b}H_{c})
intersec N m(E_{a}H_{a}) m(H_{b}H_{c}) 
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 A such that E_{a}A/E_{a}H=-1
towards A E_{a} H -1 
cmark_t A
color 200 200 200
drawsegment H A 
color 0 0 0


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

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



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



drawsegment A B
drawsegment A C
drawsegment B C

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