Construction in GCLC language

dim 120 120

point C 110 40
point M_{b} 95 67.5
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_b C
cmark_rt M_{b}
cmark_r N
color 0 0 0
fontsize 10


% Constructing a point A such that CA/CM_{b}=2
towards A C M_{b} 2 
cmark_t A
color 200 200 200
drawsegment C A 
color 0 0 0


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

color 200 200 200
drawline b
color 0 0 0



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

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



% NDG:  points C 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 C
circle k(M_{b},C) M_{b} C 

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_{\_G31672} which is a foot of the point N on the line b
foot P_{\_G31672} N b 
cmark_r P_{\_G31672}
color 200 200 200
drawline N P_{\_G31672} 
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_{\_G31672}
sim H_{b} P_{\_G31672} 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 C and H_{a} are not the same
% Constructing a line a which passes through point C and point H_{a}
line a C H_{a} 

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  lines h_{b} and 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 C and M_{b} are not the same
% Determination conditions:  lines h_{b} and a are not the same; points C 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 M_{b} and N are not the same; points C and M_{b} are not the same