Construction in GCLC language

dim 120 120

point C 110 40
point E_{a} 80 83.86
point M_{b} 95 67.5

color 220 0 0
fontsize 11

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


% Constructing a point A such that CA/CM_{b}=2
towards A C M_{b} 2 
cmark_t A
color 200 200 200
drawsegment C 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 C and H are not the same
% Constructing a line h_{c} which passes through point C and point H
line h_{c} C H 

color 200 200 200
drawline h_{c}
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 C and M_{b} are not the same
% Constructing a circle k(M_{b},C) whose center is at point M_{b} and which passes through point C
circle k(M_{b},C) M_{b} C 

color 200 200 200
drawcircle k(M_{b},C)
color 0 0 0



% NDG:  line h_{c} and circle k(M_{b},C) intersect% DET:  points C and H_{c} must be different
% Constructing a point P_{\_G27767} which is a foot of the point M_{b} on the line h_{c}
foot P_{\_G27767} M_{b} h_{c} 
cmark_r P_{\_G27767}
color 200 200 200
drawline M_{b} P_{\_G27767} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point C in the symmetry to point/line P_{\_G27767}
sim H_{c} P_{\_G27767} C 
cmark_lt H_{c}


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

color 200 200 200
drawline c
color 0 0 0



% NDG:  line h_{a} and circle k(M_{b},C) intersect% DET:  points A and H_{a} must be different
% Constructing a point P_{\_G28005} which is a foot of the point M_{b} on the line h_{a}
foot P_{\_G28005} M_{b} h_{a} 
cmark_r P_{\_G28005}
color 200 200 200
drawline M_{b} P_{\_G28005} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point A in the symmetry to point/line P_{\_G28005}
sim H_{a} P_{\_G28005} A 
cmark_b H_{a}


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

color 200 200 200
drawline a
color 0 0 0



% NDG:  lines c and a are not parallel% DET:  lines c and a are not the same
% Constructing a point B which belongs to line c and line a
intersec B c a 
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

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