Construction in GCLC language

dim 120 120

point H_{a} 80 40
point T_{a} 70.86 40

color 220 0 0
fontsize 11

cmark_b H_{a}
cmark_b T_{a}
color 0 0 0
fontsize 10


% point E_{a} is given by the problem setting, but it has to belong to the line h_{a} which is constructible from the others objects given 
% DET:  points H_{a} and T_{a} are not the same
% Constructing a line a which passes through point H_{a} and point T_{a}
line a H_{a} T_{a} 

color 200 200 200
drawline a
color 0 0 0




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

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




% Constructing a point P_{\_G58076} with coordinates (10,30)
point P_{\_G58076} 10 30 
cmark_r P_{\_G58076}

% Constructing a line L_{\_G58079} which passes through point T_{a} and point H_{a}
line L_{\_G58079} T_{a} H_{a} 

color 200 200 200
drawline L_{\_G58079}
color 0 0 0


% Constructing a line L_{\_G58082} which is perpendicular to line L_{\_G58079} and which passes through point H_{a}
perp L_{\_G58082} H_{a} L_{\_G58079} 

color 200 200 200
drawline L_{\_G58082}
color 0 0 0


% Constructing a line L_{\_G58085} which passes through point T_{a} and point P_{\_G58076}
line L_{\_G58085} T_{a} P_{\_G58076} 

color 200 200 200
drawline L_{\_G58085}
color 0 0 0


% Constructing a point E_{a} which belongs to line L_{\_G58085} and line L_{\_G58082}
intersec E_{a} L_{\_G58085} L_{\_G58082} 
color 220 0 0
fontsize 11
cmark_r E_{a}
color 0 0 0
fontsize 10




% Constructing a point A such that E_{a}A/E_{a}H_{a}=0.2313543481589756
towards A E_{a} H_{a} 0.2313543481589756 
cmark_t A
color 200 200 200
drawsegment E_{a} H_{a} 
color 0 0 0



% Constructing a point H such that AH/AE_{a}=2
towards H A E_{a} 2 
cmark_rt H
color 200 200 200
drawsegment A H 
color 0 0 0


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

color 200 200 200
drawline s_{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[_G58610] which is equal to the angle E_{a}AT_{a}
angle_o V[_G58610] E_{a} A T_{a} 


% Calculating value angle[_G58689] using formula 1/pow(2,0)*V[_G58610]+0/pow(2,0)*180
expression angle[_G58689]  { 1/pow(2,0)*V[_G58610]+0/pow(2,0)*180  } 


% Constructing a point P_{\_G58686} which is an image of the point T_{a} in a rotation around the point A for the angle 1/pow(2,0)*V[_G58610]+0/pow(2,0)*180
rotate P_{\_G58686} A angle[_G58689] T_{a} 
cmark_r P_{\_G58686}
color 200 200 200
drawarc_p A T_{a} angle[_G58689] 
color 0 0 0

% Constructing a line AO which passes through point A and point P_{\_G58686}
line AO A P_{\_G58686} 

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_{\_G59205} which passes through point M_{a} and point A
line L_{\_G59205} M_{a} A 

color 200 200 200
drawline L_{\_G59205}
color 0 0 0


% Constructing a point P_{\_G59306} with coordinates (0,0)
point P_{\_G59306} 0 0 
cmark_r P_{\_G59306}

% Constructing a point P_{\_G59230} such that M_{a}P_{\_G59230}/M_{a}P_{\_G59306}=1
towards P_{\_G59230} M_{a} P_{\_G59306} 1 
cmark_r P_{\_G59230}
color 200 200 200
drawsegment M_{a} P_{\_G59230} 
color 0 0 0

% Constructing a point P_{\_G59275} such that M_{a}P_{\_G59275}/M_{a}P_{\_G59306}=3
towards P_{\_G59275} M_{a} P_{\_G59306} 3 
cmark_r P_{\_G59275}
color 200 200 200
drawsegment M_{a} P_{\_G59275} 
color 0 0 0

% Constructing a line L_{\_G59236} which passes through point A and point P_{\_G59275}
line L_{\_G59236} A P_{\_G59275} 

color 200 200 200
drawline L_{\_G59236}
color 0 0 0


% Constructing a line L_{\_G59199} which contains the point P_{\_G59230} and is parallel to the line L_{\_G59236}
parallel L_{\_G59199} P_{\_G59230} L_{\_G59236} 

color 200 200 200
drawline L_{\_G59199}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G59199} and line L_{\_G59205}
intersec G L_{\_G59199} L_{\_G59205} 
cmark_t G



% Constructing a point O such that HO/HG=1.5
towards O H G 1.5 
cmark_t O
color 200 200 200
drawsegment H O 
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(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
% Determination conditions:  lines m(H_{b}H_{c}) and a are not the same; points A and T_{a} are not the same; points A and T_{a} are not the same; points H_{a} and T_{a} are not the same