Construction in GCLC language

dim 120 120

point H_{c} 68.91 84.83
point T_{c} 55.38 72.43

color 220 0 0
fontsize 11

cmark_lt H_{c}
cmark_lt T_{c}
color 0 0 0
fontsize 10


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

color 200 200 200
drawline c
color 0 0 0




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

color 200 200 200
drawline h_{c}
color 0 0 0




% Constructing a point P_{\_G45455} with coordinates (10,30)
point P_{\_G45455} 10 30 
cmark_r P_{\_G45455}

% Constructing a line L_{\_G45458} which passes through point T_{c} and point H_{c}
line L_{\_G45458} T_{c} H_{c} 

color 200 200 200
drawline L_{\_G45458}
color 0 0 0


% Constructing a line L_{\_G45461} which is perpendicular to line L_{\_G45458} and which passes through point H_{c}
perp L_{\_G45461} H_{c} L_{\_G45458} 

color 200 200 200
drawline L_{\_G45461}
color 0 0 0


% Constructing a line L_{\_G45464} which passes through point T_{c} and point P_{\_G45455}
line L_{\_G45464} T_{c} P_{\_G45455} 

color 200 200 200
drawline L_{\_G45464}
color 0 0 0


% Constructing a point C which belongs to line L_{\_G45464} and line L_{\_G45461}
intersec C L_{\_G45464} L_{\_G45461} 
color 220 0 0
fontsize 11
cmark_b C
color 0 0 0
fontsize 10



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

color 200 200 200
drawline s_{c}
color 0 0 0



% NDG:  points C and T_{c} are not the same; points H_{c} and C are not the same% DET:  points C and T_{c} are not the same
% Constructing an angle V[_G45830] which is equal to the angle H_{c}CT_{c}
angle_o V[_G45830] H_{c} C T_{c} 


% Calculating value angle[_G45909] using formula 1/pow(2,0)*V[_G45830]+0/pow(2,0)*180
expression angle[_G45909]  { 1/pow(2,0)*V[_G45830]+0/pow(2,0)*180  } 


% Constructing a point P_{\_G45906} which is an image of the point T_{c} in a rotation around the point C for the angle 1/pow(2,0)*V[_G45830]+0/pow(2,0)*180
rotate P_{\_G45906} C angle[_G45909] T_{c} 
cmark_r P_{\_G45906}
color 200 200 200
drawarc_p C T_{c} angle[_G45909] 
color 0 0 0

% Constructing a line CO which passes through point C and point P_{\_G45906}
line CO C P_{\_G45906} 

color 200 200 200
drawline CO
color 0 0 0




% Constructing a point A such that H_{c}A/H_{c}T_{c}=0.21698752846206876
towards A H_{c} T_{c} 0.21698752846206876 
cmark_t A
color 200 200 200
drawsegment H_{c} T_{c} 
color 0 0 0



% Constructing a point M_{b} such that AM_{b}/AC=0.5
towards M_{b} A C 0.5 
cmark_rt M_{b}
color 200 200 200
drawsegment A C 
color 0 0 0


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

color 200 200 200
drawline b
color 0 0 0




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

color 200 200 200
drawline m_{b}
color 0 0 0



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


% 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 c and circle k(O,C) intersect% DET:  points A and B must be different
% Constructing a point P_{\_G46626} which is a foot of the point O on the line c
foot P_{\_G46626} O c 
cmark_r P_{\_G46626}
color 200 200 200
drawline O P_{\_G46626} 
color 0 0 0

% Constructing a point B which is an image of the point A in the symmetry to point/line P_{\_G46626}
sim B P_{\_G46626} A 
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

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