Construction in GCLC language

dim 120 120

point M_{a} 65 40
point T_{a} 70.86 40

color 220 0 0
fontsize 11

cmark_b M_{a}
cmark_b T_{a}
color 0 0 0
fontsize 10


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

color 200 200 200
drawline 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 point P_{\_G43170} with coordinates (10,30)
point P_{\_G43170} 10 30 
cmark_r P_{\_G43170}

% Constructing a line L_{\_G43173} which passes through point T_{a} and point M_{a}
line L_{\_G43173} T_{a} M_{a} 

color 200 200 200
drawline L_{\_G43173}
color 0 0 0


% Constructing a line L_{\_G43176} which is perpendicular to line L_{\_G43173} and which passes through point M_{a}
perp L_{\_G43176} M_{a} L_{\_G43173} 

color 200 200 200
drawline L_{\_G43176}
color 0 0 0


% Constructing a line L_{\_G43179} which passes through point T_{a} and point P_{\_G43170}
line L_{\_G43179} T_{a} P_{\_G43170} 

color 200 200 200
drawline L_{\_G43179}
color 0 0 0


% Constructing a point O which belongs to line L_{\_G43179} and line L_{\_G43176}
intersec O L_{\_G43179} L_{\_G43176} 
color 220 0 0
fontsize 11
cmark_t O
color 0 0 0
fontsize 10




% Constructing a point B such that M_{a}B/M_{a}T_{a}=0.908801285307185
towards B M_{a} T_{a} 0.908801285307185 
cmark_b B
color 200 200 200
drawsegment M_{a} T_{a} 
color 0 0 0



% Constructing a point C such that BC/BM_{a}=2
towards C B M_{a} 2 
cmark_b C
color 200 200 200
drawsegment B C 
color 0 0 0


% 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 m_{a} and circle k(O,C) intersect
% Constructing points N_{a} and N_{ak} which are in intersection of k(O,C) and m_{a}
intersec2 N_{a} N_{ak} k(O,C) m_{a} 
cmark_b N_{a}
cmark_r N_{ak}


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

color 200 200 200
drawline s_{a}
color 0 0 0



% NDG:  line s_{a} and circle k(O,C) intersect% DET:  points N_{a} and A must be different
% Constructing a point P_{\_G43834} which is a foot of the point O on the line s_{a}
foot P_{\_G43834} O s_{a} 
cmark_r P_{\_G43834}
color 200 200 200
drawline O P_{\_G43834} 
color 0 0 0

% Constructing a point A which is an image of the point N_{a} in the symmetry to point/line P_{\_G43834}
sim A P_{\_G43834} N_{a} 
cmark_t A



drawsegment A B
drawsegment A C
drawsegment B C

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