Construction in GCLC language

dim 120 120

point B 20 40
point C 110 40
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_b B
cmark_b C
cmark_r N
color 0 0 0
fontsize 10


% Constructing a point M_{a} such that BM_{a}/BC=0.5
towards M_{a} B C 0.5 
cmark_b M_{a}
color 200 200 200
drawsegment B C 
color 0 0 0


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

color 200 200 200
drawline a
color 0 0 0



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

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



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

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



% NDG:  points M_{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 M_{a}
circle k(N,M_{a}) N M_{a} 

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



% NDG:  line a and circle k(N,M_{a}) intersect% DET:  points M_{a} and H_{a} must be different
% Constructing a point P_{\_G9914} which is a foot of the point N on the line a
foot P_{\_G9914} N a 
cmark_r P_{\_G9914}
color 200 200 200
drawline N P_{\_G9914} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point M_{a} in the symmetry to point/line P_{\_G9914}
sim H_{a} P_{\_G9914} M_{a} 
cmark_b H_{a}


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


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

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



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


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

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



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



% Constructing a line L_{\_G10416} which passes through point N and point H
line L_{\_G10416} N H 

color 200 200 200
drawline L_{\_G10416}
color 0 0 0


% Constructing a point P_{\_G10517} with coordinates (0,0)
point P_{\_G10517} 0 0 
cmark_r P_{\_G10517}

% Constructing a point P_{\_G10441} such that NP_{\_G10441}/NP_{\_G10517}=-1
towards P_{\_G10441} N P_{\_G10517} -1 
cmark_r P_{\_G10441}
color 200 200 200
drawsegment P_{\_G10517} P_{\_G10441} 
color 0 0 0

% Constructing a point P_{\_G10486} such that NP_{\_G10486}/NP_{\_G10517}=3
towards P_{\_G10486} N P_{\_G10517} 3 
cmark_r P_{\_G10486}
color 200 200 200
drawsegment N P_{\_G10486} 
color 0 0 0

% Constructing a line L_{\_G10447} which passes through point H and point P_{\_G10486}
line L_{\_G10447} H P_{\_G10486} 

color 200 200 200
drawline L_{\_G10447}
color 0 0 0


% Constructing a line L_{\_G10410} which contains the point P_{\_G10441} and is parallel to the line L_{\_G10447}
parallel L_{\_G10410} P_{\_G10441} L_{\_G10447} 

color 200 200 200
drawline L_{\_G10410}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G10410} and line L_{\_G10416}
intersec G L_{\_G10410} L_{\_G10416} 
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 A such that BA/BM_{c}=2
towards A B M_{c} 2 
cmark_t A
color 200 200 200
drawsegment B A 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

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