Construction in GCLC language

dim 120 120

point M_{b} 95 67.5
point M_{c} 50 67.5
point H_{c} 68.91 84.83

color 220 0 0
fontsize 11

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

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

color 200 200 200
drawline 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 c and circle k(M_{b},C) intersect% DET:  points H_{c} and A must be different
% Constructing a point P_{\_G39547} which is a foot of the point M_{b} on the line c
foot P_{\_G39547} M_{b} c 
cmark_r P_{\_G39547}
color 200 200 200
drawline M_{b} P_{\_G39547} 
color 0 0 0

% Constructing a point A which is an image of the point H_{c} in the symmetry to point/line P_{\_G39547}
sim A P_{\_G39547} H_{c} 
cmark_t A



% Constructing a point C such that AC/AM_{b}=2
towards C A M_{b} 2 
cmark_b C
color 200 200 200
drawsegment A C 
color 0 0 0



% Constructing a point B such that M_{c}B/M_{c}A=-1
towards B M_{c} A -1 
cmark_b B
color 200 200 200
drawsegment A B 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

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