Construction in GCLC language

dim 120 120

point H_{b} 89.36 77.83
point H 80 72.73

color 220 0 0
fontsize 11

cmark_rt H_{b}
cmark_rt H
color 0 0 0
fontsize 10


% point M_{b} is given by the problem setting, but it has to belong to the line b which is constructible from the others objects given 
% DET:  points H_{b} and H are not the same
% Constructing a line h_{b} which passes through point H_{b} and point H
line h_{b} H_{b} H 

color 200 200 200
drawline h_{b}
color 0 0 0




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

color 200 200 200
drawline b
color 0 0 0




% Constructing a point P_{\_G42411} with coordinates (10,30)
point P_{\_G42411} 10 30 
cmark_r P_{\_G42411}

% Constructing a line L_{\_G42414} which passes through point H and point H_{b}
line L_{\_G42414} H H_{b} 

color 200 200 200
drawline L_{\_G42414}
color 0 0 0


% Constructing a line L_{\_G42417} which is perpendicular to line L_{\_G42414} and which passes through point H_{b}
perp L_{\_G42417} H_{b} L_{\_G42414} 

color 200 200 200
drawline L_{\_G42417}
color 0 0 0


% Constructing a line L_{\_G42420} which passes through point H and point P_{\_G42411}
line L_{\_G42420} H P_{\_G42411} 

color 200 200 200
drawline L_{\_G42420}
color 0 0 0


% Constructing a point M_{b} which belongs to line L_{\_G42420} and line L_{\_G42417}
intersec M_{b} L_{\_G42420} L_{\_G42417} 
color 220 0 0
fontsize 11
cmark_rt M_{b}
color 0 0 0
fontsize 10




% Constructing a point A such that M_{b}A/M_{b}H_{b}=0.08733113667421605
towards A M_{b} H_{b} 0.08733113667421605 
cmark_t A
color 200 200 200
drawsegment M_{b} H_{b} 
color 0 0 0



% 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


% 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_{b} are not the same
% Constructing a circle k(M_{b},C) whose center is at point M_{b} and which passes through point A
circle k(M_{b},C) M_{b} A 

color 200 200 200
drawcircle k(M_{b},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_{\_G43103} which is a foot of the point M_{b} on the line h_{a}
foot P_{\_G43103} M_{b} h_{a} 
cmark_r P_{\_G43103}
color 200 200 200
drawline M_{b} P_{\_G43103} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point A in the symmetry to point/line P_{\_G43103}
sim H_{a} P_{\_G43103} 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 h_{b} and a are not parallel% DET:  lines h_{b} and a are not the same
% Constructing a point B which belongs to line h_{b} and line a
intersec B h_{b} a 
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

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