Construction in GCLC language

dim 120 120

point C 110 40
point M_{a} 65 40
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_b C
cmark_b M_{a}
cmark_r N
color 0 0 0
fontsize 10


% Constructing a point B such that CB/CM_{a}=2
towards B C M_{a} 2 
cmark_b B
color 200 200 200
drawsegment C B 
color 0 0 0


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

color 200 200 200
drawline a
color 0 0 0



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

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



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

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_{\_G23870} which is a foot of the point N on the line a
foot P_{\_G23870} N a 
cmark_r P_{\_G23870}
color 200 200 200
drawline N P_{\_G23870} 
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_{\_G23870}
sim H_{a} P_{\_G23870} 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 C and H_{b} are not the same
% Constructing a line b which passes through point C and point H_{b}
line b C H_{b} 

color 200 200 200
drawline b
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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