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 M_{a} is given by the problem setting, but it has to belong to the line 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 point M_{a} such that H_{a}M_{a}/H_{a}T_{a}=0.7971928890279072
towards M_{a} H_{a} T_{a} 0.7971928890279072 
color 220 0 0
fontsize 11
cmark_b M_{a}
color 0 0 0
fontsize 10

color 200 200 200
drawsegment H_{a} T_{a} 
color 0 0 0



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

color 200 200 200
drawline m_{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_{\_G61184} with coordinates (10,30)
point P_{\_G61184} 10 30 
cmark_r P_{\_G61184}

% Constructing a line L_{\_G61187} which passes through point M_{a} and point H_{a}
line L_{\_G61187} M_{a} H_{a} 

color 200 200 200
drawline L_{\_G61187}
color 0 0 0


% Constructing a line L_{\_G61190} which is perpendicular to line L_{\_G61187} and which passes through point H_{a}
perp L_{\_G61190} H_{a} L_{\_G61187} 

color 200 200 200
drawline L_{\_G61190}
color 0 0 0


% Constructing a line L_{\_G61193} which passes through point M_{a} and point P_{\_G61184}
line L_{\_G61193} M_{a} P_{\_G61184} 

color 200 200 200
drawline L_{\_G61193}
color 0 0 0


% Constructing a point A which belongs to line L_{\_G61193} and line L_{\_G61190}
intersec A L_{\_G61193} L_{\_G61190} 
cmark_t A


% 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:  lines m_{a} and s_{a} are not parallel% DET:  lines m_{a} and s_{a} are not the same
% Constructing a point N_{a} which belongs to line m_{a} and line s_{a}
intersec N_{a} m_{a} s_{a} 
cmark_b N_{a}


% DET:  points A and N_{a} are not the same
% Constructing bisector m(AN_{a}) of the segment AN_{a}
med m(AN_{a}) A N_{a} 

color 200 200 200
drawline m(AN_{a})
color 0 0 0

color 200 200 200
drawsegment A N_{a} 
color 0 0 0


% NDG:  lines m(AN_{a}) and m_{a} are not parallel% DET:  lines m(AN_{a}) and m_{a} are not the same
% Constructing a point O which belongs to line m(AN_{a}) and line m_{a}
intersec O m(AN_{a}) m_{a} 
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 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(AN_{a}) and m_{a} are not parallel; lines m_{a} and s_{a} are not parallel
% Determination conditions:  lines m(AN_{a}) and m_{a} are not the same; points A and N_{a} are not the same; lines m_{a} and s_{a} are not the same; points A and T_{a} are not the same; points H_{a} and T_{a} are not the same