Construction in GCLC language

dim 120 120

point A 80 95
point E_{a} 80 83.86
point T_{a} 70.86 40

color 220 0 0
fontsize 11

cmark_t A
cmark_r E_{a}
cmark_b T_{a}
color 0 0 0
fontsize 10


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

color 200 200 200
drawline h_{a}
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




% 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:  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[_G9766] which is equal to the angle E_{a}AT_{a}
angle_o V[_G9766] E_{a} A T_{a} 


% Calculating value angle[_G9845] using formula 1/pow(2,0)*V[_G9766]+0/pow(2,0)*180
expression angle[_G9845]  { 1/pow(2,0)*V[_G9766]+0/pow(2,0)*180  } 


% Constructing a point P_{\_G9842} which is an image of the point T_{a} in a rotation around the point A for the angle 1/pow(2,0)*V[_G9766]+0/pow(2,0)*180
rotate P_{\_G9842} A angle[_G9845] T_{a} 
cmark_r P_{\_G9842}
color 200 200 200
drawarc_p A T_{a} angle[_G9845] 
color 0 0 0

% Constructing a line AO which passes through point A and point P_{\_G9842}
line AO A P_{\_G9842} 

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_{\_G10359} which passes through point M_{a} and point A
line L_{\_G10359} M_{a} A 

color 200 200 200
drawline L_{\_G10359}
color 0 0 0


% Constructing a point P_{\_G10460} with coordinates (0,0)
point P_{\_G10460} 0 0 
cmark_r P_{\_G10460}

% Constructing a point P_{\_G10384} such that M_{a}P_{\_G10384}/M_{a}P_{\_G10460}=1
towards P_{\_G10384} M_{a} P_{\_G10460} 1 
cmark_r P_{\_G10384}
color 200 200 200
drawsegment M_{a} P_{\_G10384} 
color 0 0 0

% Constructing a point P_{\_G10429} such that M_{a}P_{\_G10429}/M_{a}P_{\_G10460}=3
towards P_{\_G10429} M_{a} P_{\_G10460} 3 
cmark_r P_{\_G10429}
color 200 200 200
drawsegment M_{a} P_{\_G10429} 
color 0 0 0

% Constructing a line L_{\_G10390} which passes through point A and point P_{\_G10429}
line L_{\_G10390} A P_{\_G10429} 

color 200 200 200
drawline L_{\_G10390}
color 0 0 0


% Constructing a line L_{\_G10353} which contains the point P_{\_G10384} and is parallel to the line L_{\_G10390}
parallel L_{\_G10353} P_{\_G10384} L_{\_G10390} 

color 200 200 200
drawline L_{\_G10353}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G10353} and line L_{\_G10359}
intersec G L_{\_G10353} L_{\_G10359} 
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 A and E_{a} are not the same