Construction in GCLC language

dim 120 120

point C 110 40
point E_{b} 50 56.36
point M_{a} 65 40

color 220 0 0
fontsize 11

cmark_b C
cmark_r E_{b}
cmark_b M_{a}
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



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


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

color 200 200 200
drawline h_{c}
color 0 0 0



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

color 200 200 200
drawline h_{b}
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:  line h_{c} and circle k(M_{a},B) intersect% DET:  points C and H_{c} must be different
% Constructing a point P_{\_G16729} which is a foot of the point M_{a} on the line h_{c}
foot P_{\_G16729} M_{a} h_{c} 
cmark_r P_{\_G16729}
color 200 200 200
drawline M_{a} P_{\_G16729} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point C in the symmetry to point/line P_{\_G16729}
sim H_{c} P_{\_G16729} C 
cmark_lt H_{c}


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

color 200 200 200
drawline c
color 0 0 0



% NDG:  line h_{b} and circle k(M_{a},B) intersect% DET:  points B and H_{b} must be different
% Constructing a point P_{\_G16967} which is a foot of the point M_{a} on the line h_{b}
foot P_{\_G16967} M_{a} h_{b} 
cmark_r P_{\_G16967}
color 200 200 200
drawline M_{a} P_{\_G16967} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point B in the symmetry to point/line P_{\_G16967}
sim H_{b} P_{\_G16967} B 
cmark_rt H_{b}


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

color 200 200 200
drawline b
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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