Construction in GCLC language

dim 120 120

point E_{b} 50 56.36
point H 80 72.73
point T_{b} 94.25 68.88

color 220 0 0
fontsize 11

cmark_r E_{b}
cmark_rt H
cmark_rt T_{b}
color 0 0 0
fontsize 10


% 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 E_{b} and H are not the same
% Constructing a line h_{b} which passes through point E_{b} and point H
line h_{b} E_{b} H 

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



% DET:  points T_{b} and B are not the same
% Constructing a line s_{b} which passes through point T_{b} and point B
line s_{b} T_{b} B 

color 200 200 200
drawline s_{b}
color 0 0 0




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

color 200 200 200
drawline b
color 0 0 0



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


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

color 200 200 200
drawline m(HH_{b})
color 0 0 0

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


% NDG:  points B and T_{b} are not the same; points E_{b} and B are not the same% DET:  points B and T_{b} are not the same
% Constructing an angle V[_G38813] which is equal to the angle E_{b}BT_{b}
angle_o V[_G38813] E_{b} B T_{b} 


% Calculating value angle[_G38892] using formula 1/pow(2,0)*V[_G38813]+0/pow(2,0)*180
expression angle[_G38892]  { 1/pow(2,0)*V[_G38813]+0/pow(2,0)*180  } 


% Constructing a point P_{\_G38889} which is an image of the point T_{b} in a rotation around the point B for the angle 1/pow(2,0)*V[_G38813]+0/pow(2,0)*180
rotate P_{\_G38889} B angle[_G38892] T_{b} 
cmark_r P_{\_G38889}
color 200 200 200
drawarc_p B T_{b} angle[_G38892] 
color 0 0 0

% Constructing a line BO which passes through point B and point P_{\_G38889}
line BO B P_{\_G38889} 

color 200 200 200
drawline BO
color 0 0 0




% Constructing a line m(H_{a}H_{c}) which contains the point E_{b} and is parallel to the line BO
parallel m(H_{a}H_{c}) E_{b} BO 

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



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



% Constructing a line L_{\_G39408} which passes through point M_{b} and point B
line L_{\_G39408} M_{b} B 

color 200 200 200
drawline L_{\_G39408}
color 0 0 0


% Constructing a point P_{\_G39509} with coordinates (0,0)
point P_{\_G39509} 0 0 
cmark_r P_{\_G39509}

% Constructing a point P_{\_G39433} such that M_{b}P_{\_G39433}/M_{b}P_{\_G39509}=1
towards P_{\_G39433} M_{b} P_{\_G39509} 1 
cmark_r P_{\_G39433}
color 200 200 200
drawsegment M_{b} P_{\_G39433} 
color 0 0 0

% Constructing a point P_{\_G39478} such that M_{b}P_{\_G39478}/M_{b}P_{\_G39509}=3
towards P_{\_G39478} M_{b} P_{\_G39509} 3 
cmark_r P_{\_G39478}
color 200 200 200
drawsegment M_{b} P_{\_G39478} 
color 0 0 0

% Constructing a line L_{\_G39439} which passes through point B and point P_{\_G39478}
line L_{\_G39439} B P_{\_G39478} 

color 200 200 200
drawline L_{\_G39439}
color 0 0 0


% Constructing a line L_{\_G39402} which contains the point P_{\_G39433} and is parallel to the line L_{\_G39439}
parallel L_{\_G39402} P_{\_G39433} L_{\_G39439} 

color 200 200 200
drawline L_{\_G39402}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G39402} and line L_{\_G39408}
intersec G L_{\_G39402} L_{\_G39408} 
cmark_t G



% Constructing a point N such that HN/HG=0.75
towards N H G 0.75 
cmark_r N
color 200 200 200
drawsegment H G 
color 0 0 0


% NDG:  points E_{b} and N are not the same
% Constructing a circle k(N,M_{a}) whose center is at point N and which passes through point E_{b}
circle k(N,M_{a}) N E_{b} 

color 200 200 200
drawcircle k(N,M_{a})
color 0 0 0



% NDG:  line m(HH_{b}) and circle k(N,M_{a}) intersect
% Constructing points E_{a} and E_{c} which are in intersection of k(N,M_{a}) and m(HH_{b})
intersec2 E_{a} E_{c} k(N,M_{a}) m(HH_{b}) 
cmark_r E_{a}
cmark_r E_{c}



% 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



% Constructing a point C such that HC/HE_{c}=2
towards C H E_{c} 2 
cmark_b C
color 200 200 200
drawsegment H C 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

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