Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point E_{b} 50 56.36
point M_{c} 50 67.5

color 220 0 0
fontsize 11

cmark_r E_{a}
cmark_r E_{b}
cmark_lt M_{c}
color 0 0 0
fontsize 10

% DET:  points E_{b} and M_{c} are not the same
% Constructing a line m(BH_{a}) which passes through point E_{b} and point M_{c}
line m(BH_{a}) E_{b} M_{c} 

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



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

color 200 200 200
drawline m(E_{a}E_{b})
color 0 0 0

color 200 200 200
drawsegment E_{a} E_{b} 
color 0 0 0


% DET:  points E_{a} and M_{c} are not the same
% Constructing bisector m(E_{a}M_{c}) of the segment E_{a}M_{c}
med m(E_{a}M_{c}) E_{a} M_{c} 

color 200 200 200
drawline m(E_{a}M_{c})
color 0 0 0

color 200 200 200
drawsegment E_{a} M_{c} 
color 0 0 0


% NDG:  lines m(E_{a}M_{c}) and m(E_{a}E_{b}) are not parallel% DET:  lines m(E_{a}M_{c}) and m(E_{a}E_{b}) are not the same
% Constructing a point N which belongs to line m(E_{a}M_{c}) and line m(E_{a}E_{b})
intersec N m(E_{a}M_{c}) m(E_{a}E_{b}) 
cmark_r N


% NDG:  points E_{a} and N are not the same
% Constructing a circle k(N,M_{a}) whose center is at point N and which passes through point E_{a}
circle k(N,M_{a}) N E_{a} 

color 200 200 200
drawcircle k(N,M_{a})
color 0 0 0




% Constructing a line h_{a} which contains the point E_{a} and is parallel to the line m(BH_{a})
parallel h_{a} E_{a} m(BH_{a}) 

color 200 200 200
drawline h_{a}
color 0 0 0



% NDG:  line h_{a} and circle k(N,M_{a}) intersect% DET:  points E_{a} and H_{a} must be different
% Constructing a point P_{\_G20930} which is a foot of the point N on the line h_{a}
foot P_{\_G20930} N h_{a} 
cmark_r P_{\_G20930}
color 200 200 200
drawline N P_{\_G20930} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point E_{a} in the symmetry to point/line P_{\_G20930}
sim H_{a} P_{\_G20930} E_{a} 
cmark_b H_{a}


% NDG:  points H_{a} and E_{b} are not the same
% Constructing a circle k(E_{b},B) whose center is at point E_{b} and which passes through point H_{a}
circle k(E_{b},B) E_{b} H_{a} 

color 200 200 200
drawcircle k(E_{b},B)
color 0 0 0



% NDG:  line h_{a} and circle k(E_{b},B) intersect% DET:  points H_{a} and H must be different
% Constructing a point P_{\_G21234} which is a foot of the point E_{b} on the line h_{a}
foot P_{\_G21234} E_{b} h_{a} 
cmark_r P_{\_G21234}
color 200 200 200
drawline E_{b} P_{\_G21234} 
color 0 0 0

% Constructing a point H which is an image of the point H_{a} in the symmetry to point/line P_{\_G21234}
sim H P_{\_G21234} H_{a} 
cmark_rt H



% Constructing a point A such that HA/HE_{a}=2
towards A H E_{a} 2 
cmark_t A
color 200 200 200
drawsegment H A 
color 0 0 0



% Constructing a point B such that E_{b}B/E_{b}H=-1
towards B E_{b} H -1 
cmark_b B
color 200 200 200
drawsegment H B 
color 0 0 0



% Constructing a line L_{\_G21496} which passes through point N and point H
line L_{\_G21496} N H 

color 200 200 200
drawline L_{\_G21496}
color 0 0 0


% Constructing a point P_{\_G21597} with coordinates (0,0)
point P_{\_G21597} 0 0 
cmark_r P_{\_G21597}

% Constructing a point P_{\_G21521} such that NP_{\_G21521}/NP_{\_G21597}=-1
towards P_{\_G21521} N P_{\_G21597} -1 
cmark_r P_{\_G21521}
color 200 200 200
drawsegment P_{\_G21597} P_{\_G21521} 
color 0 0 0

% Constructing a point P_{\_G21566} such that NP_{\_G21566}/NP_{\_G21597}=3
towards P_{\_G21566} N P_{\_G21597} 3 
cmark_r P_{\_G21566}
color 200 200 200
drawsegment N P_{\_G21566} 
color 0 0 0

% Constructing a line L_{\_G21527} which passes through point H and point P_{\_G21566}
line L_{\_G21527} H P_{\_G21566} 

color 200 200 200
drawline L_{\_G21527}
color 0 0 0


% Constructing a line L_{\_G21490} which contains the point P_{\_G21521} and is parallel to the line L_{\_G21527}
parallel L_{\_G21490} P_{\_G21521} L_{\_G21527} 

color 200 200 200
drawline L_{\_G21490}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G21490} and line L_{\_G21496}
intersec G L_{\_G21490} L_{\_G21496} 
cmark_t G



% Constructing a point C such that M_{c}C/M_{c}G=3
towards C M_{c} G 3 
cmark_b C
color 200 200 200
drawsegment M_{c} C 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  line h_{a} and circle k(E_{b},B) intersect; points H_{a} and E_{b} are not the same; line h_{a} and circle k(N,M_{a}) intersect; points E_{a} and N are not the same; lines m(E_{a}M_{c}) and m(E_{a}E_{b}) are not parallel
% Determination conditions:  points H_{a} and H must be different; points E_{a} and H_{a} must be different; lines m(E_{a}M_{c}) and m(E_{a}E_{b}) are not the same; points E_{a} and M_{c} are not the same; points E_{a} and E_{b} are not the same; points E_{b} and M_{c} are not the same