Construction in GCLC language

dim 120 120

point E_{b} 50 56.36
point H_{b} 89.36 77.83
point O 65 51.14

color 220 0 0
fontsize 11

cmark_r E_{b}
cmark_rt H_{b}
cmark_t O
color 0 0 0
fontsize 10

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

color 200 200 200
drawline h_{b}
color 0 0 0




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

color 200 200 200
drawline b
color 0 0 0




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

color 200 200 200
drawline m_{b}
color 0 0 0



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


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

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



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

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

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


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


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

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



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



drawsegment A B
drawsegment A C
drawsegment B C

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