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 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_{\_G29331} with coordinates (10,30)
point P_{\_G29331} 10 30 
cmark_r P_{\_G29331}

% Constructing a line L_{\_G29334} which passes through point T_{a} and point H_{a}
line L_{\_G29334} T_{a} H_{a} 

color 200 200 200
drawline L_{\_G29334}
color 0 0 0


% Constructing a line L_{\_G29337} which is perpendicular to line L_{\_G29334} and which passes through point H_{a}
perp L_{\_G29337} H_{a} L_{\_G29334} 

color 200 200 200
drawline L_{\_G29337}
color 0 0 0


% Constructing a line L_{\_G29340} which passes through point T_{a} and point P_{\_G29331}
line L_{\_G29340} T_{a} P_{\_G29331} 

color 200 200 200
drawline L_{\_G29340}
color 0 0 0


% Constructing a point A which belongs to line L_{\_G29340} and line L_{\_G29337}
intersec A L_{\_G29340} L_{\_G29337} 
color 220 0 0
fontsize 11
cmark_t A
color 0 0 0
fontsize 10



% 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 H_{a} and A are not the same% DET:  points A and T_{a} are not the same
% Constructing an angle V[_G29706] which is equal to the angle H_{a}AT_{a}
angle_o V[_G29706] H_{a} A T_{a} 


% Calculating value angle[_G29785] using formula 1/pow(2,0)*V[_G29706]+0/pow(2,0)*180
expression angle[_G29785]  { 1/pow(2,0)*V[_G29706]+0/pow(2,0)*180  } 


% Constructing a point P_{\_G29782} which is an image of the point T_{a} in a rotation around the point A for the angle 1/pow(2,0)*V[_G29706]+0/pow(2,0)*180
rotate P_{\_G29782} A angle[_G29785] T_{a} 
cmark_r P_{\_G29782}
color 200 200 200
drawarc_p A T_{a} angle[_G29785] 
color 0 0 0

% Constructing a line AO which passes through point A and point P_{\_G29782}
line AO A P_{\_G29782} 

color 200 200 200
drawline AO
color 0 0 0




% Constructing a point B such that H_{a}B/H_{a}T_{a}=0.6350811296783205
towards B H_{a} T_{a} 0.6350811296783205 
cmark_b B
color 200 200 200
drawsegment H_{a} T_{a} 
color 0 0 0



% Constructing a point M_{c} such that BM_{c}/BA=0.5
towards M_{c} B A 0.5 
cmark_lt M_{c}
color 200 200 200
drawsegment B A 
color 0 0 0


% DET:  points B and A are not the same
% Constructing a line c which passes through point B and point A
line c B A 

color 200 200 200
drawline c
color 0 0 0




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

color 200 200 200
drawline m_{c}
color 0 0 0



% NDG:  lines m_{c} and AO are not parallel% DET:  lines m_{c} and AO are not the same
% Constructing a point O which belongs to line m_{c} and line AO
intersec O m_{c} AO 
cmark_t O


% 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 a and circle k(O,C) intersect% DET:  points B and C must be different
% Constructing a point P_{\_G30502} which is a foot of the point O on the line a
foot P_{\_G30502} O a 
cmark_r P_{\_G30502}
color 200 200 200
drawline O P_{\_G30502} 
color 0 0 0

% Constructing a point C which is an image of the point B in the symmetry to point/line P_{\_G30502}
sim C P_{\_G30502} B 
cmark_b C



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  line a and circle k(O,C) intersect; points B and O are not the same; lines m_{c} and AO are not parallel; points A and T_{a} are not the same; points H_{a} and A are not the same
% Determination conditions:  points B and C must be different; lines m_{c} and AO are not the same; points B 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