Construction in GCLC language

dim 120 120

point E_{b} 50 56.36
point H_{b} 89.36 77.83
point M_{c} 50 67.5

color 220 0 0
fontsize 11

cmark_r E_{b}
cmark_rt H_{b}
cmark_lt M_{c}
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_{c} are not the same
% Constructing a circle k(M_{c},A) whose center is at point M_{c} and which passes through point H_{b}
circle k(M_{c},A) M_{c} H_{b} 

color 200 200 200
drawcircle k(M_{c},A)
color 0 0 0



% NDG:  line h_{b} and circle k(M_{c},A) intersect% DET:  points H_{b} and B must be different
% Constructing a point P_{\_G35579} which is a foot of the point M_{c} on the line h_{b}
foot P_{\_G35579} M_{c} h_{b} 
cmark_r P_{\_G35579}
color 200 200 200
drawline M_{c} P_{\_G35579} 
color 0 0 0

% Constructing a point B which is an image of the point H_{b} in the symmetry to point/line P_{\_G35579}
sim B P_{\_G35579} 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 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_{b} and A are not the same
% Constructing a line b which passes through point H_{b} and point A
line b H_{b} A 

color 200 200 200
drawline b
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(M_{c},A) intersect% DET:  points A and H_{a} must be different
% Constructing a point P_{\_G36016} which is a foot of the point M_{c} on the line h_{a}
foot P_{\_G36016} M_{c} h_{a} 
cmark_r P_{\_G36016}
color 200 200 200
drawline M_{c} P_{\_G36016} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point A in the symmetry to point/line P_{\_G36016}
sim H_{a} P_{\_G36016} A 
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 b and a are not parallel% DET:  lines b and a are not the same
% Constructing a point C which belongs to line b and line a
intersec C b a 
cmark_b C



drawsegment A B
drawsegment A C
drawsegment B C

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