Construction in GCLC language

dim 120 120

point E_{c} 95 56.36
point H 80 72.73
point M_{a} 65 40

color 220 0 0
fontsize 11

cmark_r E_{c}
cmark_rt H
cmark_b M_{a}
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 B such that M_{a}B/M_{a}C=-1
towards B M_{a} C -1 
cmark_b B
color 200 200 200
drawsegment C B 
color 0 0 0


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

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



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

color 200 200 200
drawline a
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_{b} and circle k(E_{c},C) intersect% DET:  points H and H_{b} must be different
% Constructing a point P_{\_G63167} which is a foot of the point E_{c} on the line h_{b}
foot P_{\_G63167} E_{c} h_{b} 
cmark_r P_{\_G63167}
color 200 200 200
drawline E_{c} P_{\_G63167} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point H in the symmetry to point/line P_{\_G63167}
sim H_{b} P_{\_G63167} H 
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:  line a and circle k(E_{c},C) intersect% DET:  points C and H_{a} must be different
% Constructing a point P_{\_G63405} which is a foot of the point E_{c} on the line a
foot P_{\_G63405} E_{c} a 
cmark_r P_{\_G63405}
color 200 200 200
drawline E_{c} P_{\_G63405} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point C in the symmetry to point/line P_{\_G63405}
sim H_{a} P_{\_G63405} C 
cmark_b H_{a}


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

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



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



drawsegment A B
drawsegment A C
drawsegment B C

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