Construction in GCLC language

dim 120 120

point O 65 51.14
point H_{c} 68.91 84.83
point H 80 72.73

color 220 0 0
fontsize 11

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


% Constructing a line L_{\_G33502} which passes through point O and point H
line L_{\_G33502} O H 

color 200 200 200
drawline L_{\_G33502}
color 0 0 0


% Constructing a point P_{\_G33603} with coordinates (0,0)
point P_{\_G33603} 0 0 
cmark_r P_{\_G33603}

% Constructing a point P_{\_G33527} such that OP_{\_G33527}/OP_{\_G33603}=1
towards P_{\_G33527} O P_{\_G33603} 1 
cmark_r P_{\_G33527}
color 200 200 200
drawsegment O P_{\_G33527} 
color 0 0 0

% Constructing a point P_{\_G33572} such that OP_{\_G33572}/OP_{\_G33603}=3
towards P_{\_G33572} O P_{\_G33603} 3 
cmark_r P_{\_G33572}
color 200 200 200
drawsegment O P_{\_G33572} 
color 0 0 0

% Constructing a line L_{\_G33533} which passes through point H and point P_{\_G33572}
line L_{\_G33533} H P_{\_G33572} 

color 200 200 200
drawline L_{\_G33533}
color 0 0 0


% Constructing a line L_{\_G33496} which contains the point P_{\_G33527} and is parallel to the line L_{\_G33533}
parallel L_{\_G33496} P_{\_G33527} L_{\_G33533} 

color 200 200 200
drawline L_{\_G33496}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G33496} and line L_{\_G33502}
intersec G L_{\_G33496} L_{\_G33502} 
cmark_t G


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

color 200 200 200
drawline m_{c}
color 0 0 0



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



% Constructing a point C such that M_{c}C/M_{c}G=3
towards C M_{c} G 3 
cmark_b C
color 200 200 200
drawsegment M_{c} C 
color 0 0 0


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

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



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



drawsegment A B
drawsegment A C
drawsegment B C

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