Construction in GCLC language

dim 120 120

point M_{c} 50 67.5
point T_{c} 55.38 72.43

color 220 0 0
fontsize 11

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


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

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




% Constructing a point P_{\_G47036} with coordinates (10,30)
point P_{\_G47036} 10 30 
cmark_r P_{\_G47036}

% Constructing a line L_{\_G47039} which passes through point T_{c} and point M_{c}
line L_{\_G47039} T_{c} M_{c} 

color 200 200 200
drawline L_{\_G47039}
color 0 0 0


% Constructing a line L_{\_G47042} which is perpendicular to line L_{\_G47039} and which passes through point M_{c}
perp L_{\_G47042} M_{c} L_{\_G47039} 

color 200 200 200
drawline L_{\_G47042}
color 0 0 0


% Constructing a line L_{\_G47045} which passes through point T_{c} and point P_{\_G47036}
line L_{\_G47045} T_{c} P_{\_G47036} 

color 200 200 200
drawline L_{\_G47045}
color 0 0 0


% Constructing a point O which belongs to line L_{\_G47045} and line L_{\_G47042}
intersec O L_{\_G47045} L_{\_G47042} 
color 220 0 0
fontsize 11
cmark_t O
color 0 0 0
fontsize 10




% Constructing a point A such that M_{c}A/M_{c}T_{c}=0.8854993772621633
towards A M_{c} T_{c} 0.8854993772621633 
cmark_t A
color 200 200 200
drawsegment M_{c} T_{c} 
color 0 0 0



% Constructing a point B such that AB/AM_{c}=2
towards B A M_{c} 2 
cmark_b B
color 200 200 200
drawsegment A B 
color 0 0 0


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


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

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



% NDG:  line s_{c} and circle k(O,C) intersect% DET:  points N_{c} and C must be different
% Constructing a point P_{\_G47700} which is a foot of the point O on the line s_{c}
foot P_{\_G47700} O s_{c} 
cmark_r P_{\_G47700}
color 200 200 200
drawline O P_{\_G47700} 
color 0 0 0

% Constructing a point C which is an image of the point N_{c} in the symmetry to point/line P_{\_G47700}
sim C P_{\_G47700} N_{c} 
cmark_b C



drawsegment A B
drawsegment A C
drawsegment B C

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