Construction in GCLC language

dim 120 120

point H_{c} 68.91 84.83
point H 80 72.73

color 220 0 0
fontsize 11

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


% point M_{c} is given by the problem setting, but it has to belong to the line c which is constructible from the others objects given 
% 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




% Constructing a line c which is perpendicular to line h_{c} and which passes through point H_{c}
perp c H_{c} h_{c} 

color 200 200 200
drawline c
color 0 0 0




% Constructing a point P_{\_G49831} with coordinates (10,30)
point P_{\_G49831} 10 30 
cmark_r P_{\_G49831}

% Constructing a line L_{\_G49834} which passes through point H and point H_{c}
line L_{\_G49834} H H_{c} 

color 200 200 200
drawline L_{\_G49834}
color 0 0 0


% Constructing a line L_{\_G49837} which is perpendicular to line L_{\_G49834} and which passes through point H_{c}
perp L_{\_G49837} H_{c} L_{\_G49834} 

color 200 200 200
drawline L_{\_G49837}
color 0 0 0


% Constructing a line L_{\_G49840} which passes through point H and point P_{\_G49831}
line L_{\_G49840} H P_{\_G49831} 

color 200 200 200
drawline L_{\_G49840}
color 0 0 0


% Constructing a point M_{c} which belongs to line L_{\_G49840} and line L_{\_G49837}
intersec M_{c} L_{\_G49840} L_{\_G49837} 
color 220 0 0
fontsize 11
cmark_lt M_{c}
color 0 0 0
fontsize 10




% Constructing a point A such that M_{c}A/M_{c}H_{c}=0.9184732155460466
towards A M_{c} H_{c} 0.9184732155460466 
cmark_t A
color 200 200 200
drawsegment M_{c} H_{c} 
color 0 0 0



% Constructing a point B such that AB/AM_{c}=2
towards B A M_{c} 2 
cmark_b B
color 200 200 200
drawsegment A B 
color 0 0 0


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

color 200 200 200
drawline h_{a}
color 0 0 0



% NDG:  points A and M_{c} are not the same
% Constructing a circle k(M_{c},A) whose center is at point M_{c} and which passes through point A
circle k(M_{c},A) M_{c} A 

color 200 200 200
drawcircle k(M_{c},A)
color 0 0 0



% NDG:  line h_{a} and circle k(M_{c},A) intersect% DET:  points A and H_{a} must be different
% Constructing a point P_{\_G50523} which is a foot of the point M_{c} on the line h_{a}
foot P_{\_G50523} M_{c} h_{a} 
cmark_r P_{\_G50523}
color 200 200 200
drawline M_{c} P_{\_G50523} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point A in the symmetry to point/line P_{\_G50523}
sim H_{a} P_{\_G50523} A 
cmark_b H_{a}


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



drawsegment A B
drawsegment A C
drawsegment B C

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