Construction in GCLC language

dim 120 120

point A 80 95
point C 110 40
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_t A
cmark_b C
cmark_r N
color 0 0 0
fontsize 10


% Constructing a point M_{b} such that AM_{b}/AC=0.5
towards M_{b} A C 0.5 
cmark_rt M_{b}
color 200 200 200
drawsegment A C 
color 0 0 0


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

color 200 200 200
drawline b
color 0 0 0



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

color 200 200 200
drawline m(H_{a}H_{c})
color 0 0 0



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

color 200 200 200
drawcircle k(M_{b},C)
color 0 0 0



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

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



% NDG:  line b and circle k(N,M_{a}) intersect% DET:  points M_{b} and H_{b} must be different
% Constructing a point P_{\_G6591} which is a foot of the point N on the line b
foot P_{\_G6591} N b 
cmark_r P_{\_G6591}
color 200 200 200
drawline N P_{\_G6591} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point M_{b} in the symmetry to point/line P_{\_G6591}
sim H_{b} P_{\_G6591} M_{b} 
cmark_rt H_{b}


% NDG:  line m(H_{a}H_{c}) and circle k(N,M_{a}) intersect% DET:  points M_{b} and E_{b} must be different
% Constructing a point E_{b} which is an image of the point M_{b} in the symmetry to point/line N
sim E_{b} N M_{b} 
cmark_r E_{b}


% DET:  points E_{b} and H_{b} are not the same
% Constructing a line h_{b} which passes through point E_{b} and point H_{b}
line h_{b} E_{b} H_{b} 

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



% NDG:  circles k(M_{b},C) and k(N,M_{a}) intersect% DET:  circles k(M_{b},C) and k(N,M_{a}) are not the same
% Constructing points H_{a} and H_{c} which are in intersection of k(M_{b},C) and k(N,M_{a})
intersec2 H_{a} H_{c} k(M_{b},C) k(N,M_{a}) 
cmark_b H_{a}
cmark_lt H_{c}


% DET:  points A and H_{a} are not the same
% Constructing a line h_{a} which passes through point A and point H_{a}
line h_{a} A H_{a} 

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



% NDG:  lines h_{b} and h_{a} are not parallel% DET:  lines h_{b} and h_{a} are not the same
% Constructing a point H which belongs to line h_{b} and line h_{a}
intersec H h_{b} h_{a} 
cmark_rt H



% Constructing a line L_{\_G7093} which passes through point N and point H
line L_{\_G7093} N H 

color 200 200 200
drawline L_{\_G7093}
color 0 0 0


% Constructing a point P_{\_G7194} with coordinates (0,0)
point P_{\_G7194} 0 0 
cmark_r P_{\_G7194}

% Constructing a point P_{\_G7118} such that NP_{\_G7118}/NP_{\_G7194}=-1
towards P_{\_G7118} N P_{\_G7194} -1 
cmark_r P_{\_G7118}
color 200 200 200
drawsegment P_{\_G7194} P_{\_G7118} 
color 0 0 0

% Constructing a point P_{\_G7163} such that NP_{\_G7163}/NP_{\_G7194}=3
towards P_{\_G7163} N P_{\_G7194} 3 
cmark_r P_{\_G7163}
color 200 200 200
drawsegment N P_{\_G7163} 
color 0 0 0

% Constructing a line L_{\_G7124} which passes through point H and point P_{\_G7163}
line L_{\_G7124} H P_{\_G7163} 

color 200 200 200
drawline L_{\_G7124}
color 0 0 0


% Constructing a line L_{\_G7087} which contains the point P_{\_G7118} and is parallel to the line L_{\_G7124}
parallel L_{\_G7087} P_{\_G7118} L_{\_G7124} 

color 200 200 200
drawline L_{\_G7087}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G7087} and line L_{\_G7093}
intersec G L_{\_G7087} L_{\_G7093} 
cmark_t G



% Constructing a point M_{c} such that CM_{c}/CG=1.5
towards M_{c} C G 1.5 
cmark_lt M_{c}
color 200 200 200
drawsegment C M_{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



drawsegment A B
drawsegment A C
drawsegment B C

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