Construction in GCLC language

dim 120 120

point E_{b} 50 56.36
point H 80 72.73
point M_{a} 65 40

color 220 0 0
fontsize 11

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


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



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

color 200 200 200
drawline a
color 0 0 0



% NDG:  points H 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
circle k(E_{b},B) E_{b} H 

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



% NDG:  line h_{c} and circle k(E_{b},B) intersect% DET:  points H and H_{c} must be different
% Constructing a point P_{\_G58210} which is a foot of the point E_{b} on the line h_{c}
foot P_{\_G58210} E_{b} h_{c} 
cmark_r P_{\_G58210}
color 200 200 200
drawline E_{b} P_{\_G58210} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point H in the symmetry to point/line P_{\_G58210}
sim H_{c} P_{\_G58210} H 
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 a and circle k(E_{b},B) intersect% DET:  points B and H_{a} must be different
% Constructing a point P_{\_G58448} which is a foot of the point E_{b} on the line a
foot P_{\_G58448} E_{b} a 
cmark_r P_{\_G58448}
color 200 200 200
drawline E_{b} P_{\_G58448} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point B in the symmetry to point/line P_{\_G58448}
sim H_{a} P_{\_G58448} B 
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 c and h_{a} are not parallel% DET:  lines c and h_{a} are not the same
% Constructing a point A which belongs to line c and line h_{a}
intersec A c h_{a} 
cmark_t A



drawsegment A B
drawsegment A C
drawsegment B C

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