Construction in GCLC language

dim 120 120

point M_{b} 95 67.5
point H_{c} 68.91 84.83
point H 80 72.73

color 220 0 0
fontsize 11

cmark_rt M_{b}
cmark_lt H_{c}
cmark_rt H
color 0 0 0
fontsize 10

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

color 200 200 200
drawline h_{c}
color 0 0 0



% NDG:  points H_{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 H_{c}
circle k(M_{b},C) M_{b} H_{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 H_{c} and C must be different
% Constructing a point P_{\_G48246} which is a foot of the point M_{b} on the line h_{c}
foot P_{\_G48246} M_{b} h_{c} 
cmark_r P_{\_G48246}
color 200 200 200
drawline M_{b} P_{\_G48246} 
color 0 0 0

% Constructing a point C which is an image of the point H_{c} in the symmetry to point/line P_{\_G48246}
sim C P_{\_G48246} H_{c} 
cmark_b C



% 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


% 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



% 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_{b},C) intersect% DET:  points A and H_{a} must be different
% Constructing a point P_{\_G48609} which is a foot of the point M_{b} on the line h_{a}
foot P_{\_G48609} M_{b} h_{a} 
cmark_r P_{\_G48609}
color 200 200 200
drawline M_{b} P_{\_G48609} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point A in the symmetry to point/line P_{\_G48609}
sim H_{a} P_{\_G48609} A 
cmark_b H_{a}


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

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