Construction in GCLC language

dim 120 120

point O 65 51.14
point H_{a} 80 40
point H 80 72.73

color 220 0 0
fontsize 11

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


% Constructing a line L_{\_G37761} which passes through point O and point H
line L_{\_G37761} O H 

color 200 200 200
drawline L_{\_G37761}
color 0 0 0


% Constructing a point P_{\_G37862} with coordinates (0,0)
point P_{\_G37862} 0 0 
cmark_r P_{\_G37862}

% Constructing a point P_{\_G37786} such that OP_{\_G37786}/OP_{\_G37862}=1
towards P_{\_G37786} O P_{\_G37862} 1 
cmark_r P_{\_G37786}
color 200 200 200
drawsegment O P_{\_G37786} 
color 0 0 0

% Constructing a point P_{\_G37831} such that OP_{\_G37831}/OP_{\_G37862}=3
towards P_{\_G37831} O P_{\_G37862} 3 
cmark_r P_{\_G37831}
color 200 200 200
drawsegment O P_{\_G37831} 
color 0 0 0

% Constructing a line L_{\_G37792} which passes through point H and point P_{\_G37831}
line L_{\_G37792} H P_{\_G37831} 

color 200 200 200
drawline L_{\_G37792}
color 0 0 0


% Constructing a line L_{\_G37755} which contains the point P_{\_G37786} and is parallel to the line L_{\_G37792}
parallel L_{\_G37755} P_{\_G37786} L_{\_G37792} 

color 200 200 200
drawline L_{\_G37755}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G37755} and line L_{\_G37761}
intersec G L_{\_G37755} L_{\_G37761} 
cmark_t G


% 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 line m_{a} which is perpendicular to line a and which passes through point O
perp m_{a} O a 

color 200 200 200
drawline m_{a}
color 0 0 0



% NDG:  lines m_{a} and a are not parallel% DET:  lines m_{a} and a are not the same
% Constructing a point M_{a} which belongs to line m_{a} and line a
intersec M_{a} m_{a} a 
cmark_b M_{a}



% Constructing a point A such that M_{a}A/M_{a}G=3
towards A M_{a} G 3 
cmark_t A
color 200 200 200
drawsegment M_{a} A 
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; lines m_{a} and a are not parallel
% Determination conditions:  lines m_{a} and a are not the same; points H_{a} and H are not the same