Construction in GCLC language

dim 120 120

point H_{b} 89.36 77.83
point T_{b} 94.25 68.88

color 220 0 0
fontsize 11

cmark_rt H_{b}
cmark_rt T_{b}
color 0 0 0
fontsize 10


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

color 200 200 200
drawline b
color 0 0 0




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

color 200 200 200
drawline h_{b}
color 0 0 0




% Constructing a point P_{\_G35061} with coordinates (10,30)
point P_{\_G35061} 10 30 
cmark_r P_{\_G35061}

% Constructing a line L_{\_G35064} which passes through point T_{b} and point H_{b}
line L_{\_G35064} T_{b} H_{b} 

color 200 200 200
drawline L_{\_G35064}
color 0 0 0


% Constructing a line L_{\_G35067} which is perpendicular to line L_{\_G35064} and which passes through point H_{b}
perp L_{\_G35067} H_{b} L_{\_G35064} 

color 200 200 200
drawline L_{\_G35067}
color 0 0 0


% Constructing a line L_{\_G35070} which passes through point T_{b} and point P_{\_G35061}
line L_{\_G35070} T_{b} P_{\_G35061} 

color 200 200 200
drawline L_{\_G35070}
color 0 0 0


% Constructing a point B which belongs to line L_{\_G35070} and line L_{\_G35067}
intersec B L_{\_G35070} L_{\_G35067} 
color 220 0 0
fontsize 11
cmark_b B
color 0 0 0
fontsize 10



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

color 200 200 200
drawline s_{b}
color 0 0 0



% NDG:  points B and T_{b} are not the same; points H_{b} and B are not the same% DET:  points B and T_{b} are not the same
% Constructing an angle V[_G35436] which is equal to the angle H_{b}BT_{b}
angle_o V[_G35436] H_{b} B T_{b} 


% Calculating value angle[_G35515] using formula 1/pow(2,0)*V[_G35436]+0/pow(2,0)*180
expression angle[_G35515]  { 1/pow(2,0)*V[_G35436]+0/pow(2,0)*180  } 


% Constructing a point P_{\_G35512} which is an image of the point T_{b} in a rotation around the point B for the angle 1/pow(2,0)*V[_G35436]+0/pow(2,0)*180
rotate P_{\_G35512} B angle[_G35515] T_{b} 
cmark_r P_{\_G35512}
color 200 200 200
drawarc_p B T_{b} angle[_G35515] 
color 0 0 0

% Constructing a line BO which passes through point B and point P_{\_G35512}
line BO B P_{\_G35512} 

color 200 200 200
drawline BO
color 0 0 0




% Constructing a point A such that H_{b}A/H_{b}T_{b}=0.6009102411791909
towards A H_{b} T_{b} 0.6009102411791909 
cmark_t A
color 200 200 200
drawsegment H_{b} T_{b} 
color 0 0 0



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


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

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 BO are not parallel% DET:  lines m_{c} and BO are not the same
% Constructing a point O which belongs to line m_{c} and line BO
intersec O m_{c} BO 
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 b and circle k(O,C) intersect% DET:  points A and C must be different
% Constructing a point P_{\_G36232} which is a foot of the point O on the line b
foot P_{\_G36232} O b 
cmark_r P_{\_G36232}
color 200 200 200
drawline O P_{\_G36232} 
color 0 0 0

% Constructing a point C which is an image of the point A in the symmetry to point/line P_{\_G36232}
sim C P_{\_G36232} A 
cmark_b C



drawsegment A B
drawsegment A C
drawsegment B C

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