Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point H 80 72.73
point T_{a} 70.86 40

color 220 0 0
fontsize 11

cmark_r E_{a}
cmark_rt H
cmark_b T_{a}
color 0 0 0
fontsize 10


% 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


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

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



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

color 200 200 200
drawline s_{a}
color 0 0 0




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

color 200 200 200
drawline a
color 0 0 0



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


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

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

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


% NDG:  points A and T_{a} are not the same; points E_{a} and A are not the same% DET:  points A and T_{a} are not the same
% Constructing an angle V[_G50541] which is equal to the angle E_{a}AT_{a}
angle_o V[_G50541] E_{a} A T_{a} 


% Calculating value angle[_G50620] using formula 1/pow(2,0)*V[_G50541]+0/pow(2,0)*180
expression angle[_G50620]  { 1/pow(2,0)*V[_G50541]+0/pow(2,0)*180  } 


% Constructing a point P_{\_G50617} which is an image of the point T_{a} in a rotation around the point A for the angle 1/pow(2,0)*V[_G50541]+0/pow(2,0)*180
rotate P_{\_G50617} A angle[_G50620] T_{a} 
cmark_r P_{\_G50617}
color 200 200 200
drawarc_p A T_{a} angle[_G50620] 
color 0 0 0

% Constructing a line AO which passes through point A and point P_{\_G50617}
line AO A P_{\_G50617} 

color 200 200 200
drawline AO
color 0 0 0




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

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



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



% Constructing a line L_{\_G51136} which passes through point M_{a} and point A
line L_{\_G51136} M_{a} A 

color 200 200 200
drawline L_{\_G51136}
color 0 0 0


% Constructing a point P_{\_G51237} with coordinates (0,0)
point P_{\_G51237} 0 0 
cmark_r P_{\_G51237}

% Constructing a point P_{\_G51161} such that M_{a}P_{\_G51161}/M_{a}P_{\_G51237}=1
towards P_{\_G51161} M_{a} P_{\_G51237} 1 
cmark_r P_{\_G51161}
color 200 200 200
drawsegment M_{a} P_{\_G51161} 
color 0 0 0

% Constructing a point P_{\_G51206} such that M_{a}P_{\_G51206}/M_{a}P_{\_G51237}=3
towards P_{\_G51206} M_{a} P_{\_G51237} 3 
cmark_r P_{\_G51206}
color 200 200 200
drawsegment M_{a} P_{\_G51206} 
color 0 0 0

% Constructing a line L_{\_G51167} which passes through point A and point P_{\_G51206}
line L_{\_G51167} A P_{\_G51206} 

color 200 200 200
drawline L_{\_G51167}
color 0 0 0


% Constructing a line L_{\_G51130} which contains the point P_{\_G51161} and is parallel to the line L_{\_G51167}
parallel L_{\_G51130} P_{\_G51161} L_{\_G51167} 

color 200 200 200
drawline L_{\_G51130}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G51130} and line L_{\_G51136}
intersec G L_{\_G51130} L_{\_G51136} 
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_{a} 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_{a}
circle k(N,M_{a}) N E_{a} 

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



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



% 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



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