Construction in GCLC language

dim 120 120

point H_{a} 80 40
point H 80 72.73

color 220 0 0
fontsize 11

cmark_b H_{a}
cmark_rt H
color 0 0 0
fontsize 10


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

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




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

color 200 200 200
drawline a
color 0 0 0




% Constructing a point P_{\_G59956} with coordinates (10,30)
point P_{\_G59956} 10 30 
cmark_r P_{\_G59956}

% Constructing a line L_{\_G59959} which passes through point H and point H_{a}
line L_{\_G59959} H H_{a} 

color 200 200 200
drawline L_{\_G59959}
color 0 0 0


% Constructing a line L_{\_G59962} which is perpendicular to line L_{\_G59959} and which passes through point H_{a}
perp L_{\_G59962} H_{a} L_{\_G59959} 

color 200 200 200
drawline L_{\_G59962}
color 0 0 0


% Constructing a line L_{\_G59965} which passes through point H and point P_{\_G59956}
line L_{\_G59965} H P_{\_G59956} 

color 200 200 200
drawline L_{\_G59965}
color 0 0 0


% Constructing a point M_{a} which belongs to line L_{\_G59965} and line L_{\_G59962}
intersec M_{a} L_{\_G59965} L_{\_G59962} 
color 220 0 0
fontsize 11
cmark_b M_{a}
color 0 0 0
fontsize 10




% Constructing a point A such that H_{a}A/H_{a}H=0.04428254146103481
towards A H_{a} H 0.04428254146103481 
cmark_t A
color 200 200 200
drawsegment H_{a} H 
color 0 0 0



% Constructing a line L_{\_G60333} which passes through point A and point M_{a}
line L_{\_G60333} A M_{a} 

color 200 200 200
drawline L_{\_G60333}
color 0 0 0


% Constructing a point P_{\_G60434} with coordinates (0,0)
point P_{\_G60434} 0 0 
cmark_r P_{\_G60434}

% Constructing a point P_{\_G60358} such that AP_{\_G60358}/AP_{\_G60434}=2
towards P_{\_G60358} A P_{\_G60434} 2 
cmark_r P_{\_G60358}
color 200 200 200
drawsegment A P_{\_G60358} 
color 0 0 0

% Constructing a point P_{\_G60403} such that AP_{\_G60403}/AP_{\_G60434}=3
towards P_{\_G60403} A P_{\_G60434} 3 
cmark_r P_{\_G60403}
color 200 200 200
drawsegment A P_{\_G60403} 
color 0 0 0

% Constructing a line L_{\_G60364} which passes through point M_{a} and point P_{\_G60403}
line L_{\_G60364} M_{a} P_{\_G60403} 

color 200 200 200
drawline L_{\_G60364}
color 0 0 0


% Constructing a line L_{\_G60327} which contains the point P_{\_G60358} and is parallel to the line L_{\_G60364}
parallel L_{\_G60327} P_{\_G60358} L_{\_G60364} 

color 200 200 200
drawline L_{\_G60327}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G60327} and line L_{\_G60333}
intersec G L_{\_G60327} L_{\_G60333} 
cmark_t G



% Constructing a point O such that HO/HG=1.5
towards O H G 1.5 
cmark_t O
color 200 200 200
drawsegment H O 
color 0 0 0


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

color 200 200 200
drawcircle k(O,C)
color 0 0 0



% NDG:  line a and circle k(O,C) intersect
% Constructing points C and B which are in intersection of k(O,C) and a
intersec2 C B k(O,C) a 
cmark_b C
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  line a and circle k(O,C) intersect; points A and O are not the same
% Determination conditions:  points H_{a} and H are not the same