Construction in GCLC language

dim 120 120

point E_{b} 50 56.36
point H_{c} 68.91 84.83
point M_{c} 50 67.5

color 220 0 0
fontsize 11

cmark_r E_{b}
cmark_lt H_{c}
cmark_lt M_{c}
color 0 0 0
fontsize 10

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

color 200 200 200
drawline c
color 0 0 0



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

color 200 200 200
drawcircle k(E_{b},B)
color 0 0 0



% NDG:  line c and circle k(E_{b},B) intersect% DET:  points H_{c} and B must be different
% Constructing a point P_{\_G59409} which is a foot of the point E_{b} on the line c
foot P_{\_G59409} E_{b} c 
cmark_r P_{\_G59409}
color 200 200 200
drawline E_{b} P_{\_G59409} 
color 0 0 0

% Constructing a point B which is an image of the point H_{c} in the symmetry to point/line P_{\_G59409}
sim B P_{\_G59409} H_{c} 
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 A such that M_{c}A/M_{c}B=-1
towards A M_{c} B -1 
cmark_t A
color 200 200 200
drawsegment B A 
color 0 0 0


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

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



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

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



% NDG:  line h_{a} and circle k(E_{b},B) intersect% DET:  points H and H_{a} must be different
% Constructing a point P_{\_G59846} which is a foot of the point E_{b} on the line h_{a}
foot P_{\_G59846} E_{b} h_{a} 
cmark_r P_{\_G59846}
color 200 200 200
drawline E_{b} P_{\_G59846} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point H in the symmetry to point/line P_{\_G59846}
sim H_{a} P_{\_G59846} H 
cmark_b H_{a}


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

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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