Construction in GCLC language

dim 120 120

point B 20 40
point E_{a} 80 83.86
point M_{c} 50 67.5

color 220 0 0
fontsize 11

cmark_b B
cmark_r E_{a}
cmark_lt M_{c}
color 0 0 0
fontsize 10


% Constructing a point A such that BA/BM_{c}=2
towards A B M_{c} 2 
cmark_t A
color 200 200 200
drawsegment B A 
color 0 0 0



% Constructing a point H such that E_{a}H/E_{a}A=-1
towards H E_{a} A -1 
cmark_rt H
color 200 200 200
drawsegment A H 
color 0 0 0


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

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



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

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



% NDG:  points 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 B
circle k(M_{c},A) M_{c} 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 B and H_{b} must be different
% Constructing a point P_{\_G10976} which is a foot of the point M_{c} on the line h_{b}
foot P_{\_G10976} M_{c} h_{b} 
cmark_r P_{\_G10976}
color 200 200 200
drawline M_{c} P_{\_G10976} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point B in the symmetry to point/line P_{\_G10976}
sim H_{b} P_{\_G10976} B 
cmark_rt H_{b}


% 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



% NDG:  line h_{a} and circle k(M_{c},A) intersect% DET:  points A and H_{a} must be different
% Constructing a point P_{\_G11214} which is a foot of the point M_{c} on the line h_{a}
foot P_{\_G11214} M_{c} h_{a} 
cmark_r P_{\_G11214}
color 200 200 200
drawline M_{c} P_{\_G11214} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point A in the symmetry to point/line P_{\_G11214}
sim H_{a} P_{\_G11214} A 
cmark_b H_{a}


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

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 B and M_{c} are not the same
% Determination conditions:  lines b and a are not the same; points H_{a} and B are not the same; points A and H_{a} must be different; points H_{b} and A are not the same; points B and H_{b} must be different; points E_{a} and A are not the same; points B and H are not the same