Construction in GCLC language

dim 120 120

point B 20 40
point G 70 58.33
point H_{a} 80 40

color 220 0 0
fontsize 11

cmark_b B
cmark_t G
cmark_b H_{a}
color 0 0 0
fontsize 10


% Constructing a point M_{b} such that BM_{b}/BG=1.5
towards M_{b} B G 1.5 
cmark_rt M_{b}
color 200 200 200
drawsegment B M_{b} 
color 0 0 0


% 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:  points H_{a} 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_{a}
circle k(M_{b},C) M_{b} H_{a} 

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



% NDG:  line a and circle k(M_{b},C) intersect% DET:  points H_{a} and C must be different
% Constructing a point P_{\_G17594} which is a foot of the point M_{b} on the line a
foot P_{\_G17594} M_{b} a 
cmark_r P_{\_G17594}
color 200 200 200
drawline M_{b} P_{\_G17594} 
color 0 0 0

% Constructing a point C which is an image of the point H_{a} in the symmetry to point/line P_{\_G17594}
sim C P_{\_G17594} H_{a} 
cmark_b C



% Constructing a point M_{c} such that GM_{c}/GC=-0.5
towards M_{c} G C -0.5 
cmark_lt M_{c}
color 200 200 200
drawsegment C M_{c} 
color 0 0 0



% 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



drawsegment A B
drawsegment A C
drawsegment B C

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