Construction in GCLC language

dim 120 120

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

color 220 0 0
fontsize 11

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

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

color 200 200 200
drawline a
color 0 0 0



% NDG:  points H_{a} 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_{a}
circle k(E_{b},B) E_{b} H_{a} 

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



% NDG:  line a and circle k(E_{b},B) intersect% DET:  points H_{a} and B must be different
% Constructing a point P_{\_G42447} which is a foot of the point E_{b} on the line a
foot P_{\_G42447} E_{b} a 
cmark_r P_{\_G42447}
color 200 200 200
drawline E_{b} P_{\_G42447} 
color 0 0 0

% Constructing a point B which is an image of the point H_{a} in the symmetry to point/line P_{\_G42447}
sim B P_{\_G42447} H_{a} 
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 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_{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



% 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



% NDG:  line h_{c} and circle k(E_{b},B) intersect% DET:  points H and H_{c} must be different
% Constructing a point P_{\_G42884} which is a foot of the point E_{b} on the line h_{c}
foot P_{\_G42884} E_{b} h_{c} 
cmark_r P_{\_G42884}
color 200 200 200
drawline E_{b} P_{\_G42884} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point H in the symmetry to point/line P_{\_G42884}
sim H_{c} P_{\_G42884} H 
cmark_lt H_{c}


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

color 200 200 200
drawline c
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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