Construction in GCLC language

dim 120 120

point E_{c} 95 56.36
point H 80 72.73
point M_{b} 95 67.5

color 220 0 0
fontsize 11

cmark_r E_{c}
cmark_rt H
cmark_rt M_{b}
color 0 0 0
fontsize 10


% Constructing a point C such that E_{c}C/E_{c}H=-1
towards C E_{c} H -1 
cmark_b C
color 200 200 200
drawsegment H C 
color 0 0 0



% Constructing a point A such that M_{b}A/M_{b}C=-1
towards A M_{b} C -1 
cmark_t A
color 200 200 200
drawsegment C A 
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



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

color 200 200 200
drawline b
color 0 0 0



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

color 200 200 200
drawcircle k(E_{c},C)
color 0 0 0



% NDG:  line h_{a} and circle k(E_{c},C) intersect% DET:  points H and H_{a} must be different
% Constructing a point P_{\_G37214} which is a foot of the point E_{c} on the line h_{a}
foot P_{\_G37214} E_{c} h_{a} 
cmark_r P_{\_G37214}
color 200 200 200
drawline E_{c} P_{\_G37214} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point H in the symmetry to point/line P_{\_G37214}
sim H_{a} P_{\_G37214} H 
cmark_b H_{a}


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

color 200 200 200
drawline a
color 0 0 0



% NDG:  line b and circle k(E_{c},C) intersect% DET:  points C and H_{b} must be different
% Constructing a point P_{\_G37452} which is a foot of the point E_{c} on the line b
foot P_{\_G37452} E_{c} b 
cmark_r P_{\_G37452}
color 200 200 200
drawline E_{c} P_{\_G37452} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point C in the symmetry to point/line P_{\_G37452}
sim H_{b} P_{\_G37452} C 
cmark_rt H_{b}


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

color 200 200 200
drawline h_{b}
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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