Construction in GCLC language

dim 120 120

point E_{b} 50 56.36
point H_{b} 89.36 77.83
point M_{a} 65 40

color 220 0 0
fontsize 11

cmark_r E_{b}
cmark_rt H_{b}
cmark_b M_{a}
color 0 0 0
fontsize 10

% 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:  points H_{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 H_{b}
circle k(M_{a},B) M_{a} H_{b} 

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



% NDG:  line h_{b} and circle k(M_{a},B) intersect% DET:  points H_{b} and B must be different
% Constructing a point P_{\_G32515} which is a foot of the point M_{a} on the line h_{b}
foot P_{\_G32515} M_{a} h_{b} 
cmark_r P_{\_G32515}
color 200 200 200
drawline M_{a} P_{\_G32515} 
color 0 0 0

% Constructing a point B which is an image of the point H_{b} in the symmetry to point/line P_{\_G32515}
sim B P_{\_G32515} H_{b} 
cmark_b B



% Constructing a point H such that BH/BE_{b}=2
towards H B E_{b} 2 
cmark_rt H
color 200 200 200
drawsegment B H 
color 0 0 0



% Constructing a point C such that M_{a}C/M_{a}B=-1
towards C M_{a} B -1 
cmark_b C
color 200 200 200
drawsegment B C 
color 0 0 0


% 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



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

color 200 200 200
drawline h_{c}
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_{\_G32952} which is a foot of the point M_{a} on the line h_{c}
foot P_{\_G32952} M_{a} h_{c} 
cmark_r P_{\_G32952}
color 200 200 200
drawline M_{a} P_{\_G32952} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point C in the symmetry to point/line P_{\_G32952}
sim H_{c} P_{\_G32952} C 
cmark_lt H_{c}


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

color 200 200 200
drawline c
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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