Construction in GCLC language

dim 120 120

point A 80 95
point M_{a} 65 40
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_t A
cmark_b M_{a}
cmark_b I
color 0 0 0
fontsize 10

% DET:  points M_{a} and I are not the same
% Constructing a line IM_{a} which passes through point M_{a} and point I
line IM_{a} M_{a} I 

color 200 200 200
drawline IM_{a}
color 0 0 0



% NDG:  points I and M_{a} are not the same
% Constructing midpoint P_{\_G15027} of the segment IM_{a}
midpoint P_{\_G15027} I M_{a} 
cmark_r P_{\_G15027}

% Constructing a circle k_over(I,M_{a}) whose center is at point P_{\_G15027} and which passes through point I
circle k_over(I,M_{a}) P_{\_G15027} I 

color 200 200 200
drawcircle k_over(I,M_{a})
color 0 0 0




% Constructing a line AP`_{a} which contains the point A and is parallel to the line IM_{a}
parallel AP`_{a} A IM_{a} 

color 200 200 200
drawline AP`_{a}
color 0 0 0




% Constructing a point P_{\_G15328} such that M_{a}P_{\_G15328}/M_{a}A=-1
towards P_{\_G15328} M_{a} A -1 
cmark_r P_{\_G15328}
color 200 200 200
drawsegment A P_{\_G15328} 
color 0 0 0

% Constructing a line h_{M_{a},-1/1}(AP`_{a}) which contains the point P_{\_G15328} and is parallel to the line AP`_{a}
parallel h_{M_{a},-1/1}(AP`_{a}) P_{\_G15328} AP`_{a} 

color 200 200 200
drawline h_{M_{a},-1/1}(AP`_{a})
color 0 0 0



% NDG:  line h_{M_{a},-1/1}(AP`_{a}) and circle k_over(I,M_{a}) intersect
% Constructing points A_{fo} and P_{a} which are in intersection of k_over(I,M_{a}) and h_{M_{a},-1/1}(AP`_{a})
intersec2 A_{fo} P_{a} k_over(I,M_{a}) h_{M_{a},-1/1}(AP`_{a}) 
cmark_r A_{fo}
cmark_r P_{a}


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

color 200 200 200
drawcircle k(I,P_{a})
color 0 0 0



% NDG:  point A is outside the circle k(I,P_{a})
% Constructing midpoint P_{\_G5944} of the segment AI
midpoint P_{\_G5944} A I 
cmark_r P_{\_G5944}

% Constructing a circle C_{\_G5947} whose center is at point P_{\_G5944} and which passes through point A
circle C_{\_G5947} P_{\_G5944} A 

color 200 200 200
drawcircle C_{\_G5947}
color 0 0 0


% Constructing points P_{\_G5950} and P_{\_G5953} which are in intersection of C_{\_G5947} and k(I,P_{a})
intersec2 P_{\_G5950} P_{\_G5953} C_{\_G5947} k(I,P_{a}) 
cmark_r P_{\_G5950}
cmark_r P_{\_G5953}

% Constructing a line c which passes through point A and point P_{\_G5950}
line c A P_{\_G5950} 

color 200 200 200
drawline c
color 0 0 0


% Constructing a line b which passes through point A and point P_{\_G5953}
line b A P_{\_G5953} 

color 200 200 200
drawline b
color 0 0 0



% NDG:  point M_{a} is outside the circle k(I,P_{a})
% Constructing midpoint P_{\_G6356} of the segment M_{a}I
midpoint P_{\_G6356} M_{a} I 
cmark_r P_{\_G6356}

% Constructing a circle C_{\_G6359} whose center is at point P_{\_G6356} and which passes through point M_{a}
circle C_{\_G6359} P_{\_G6356} M_{a} 

color 200 200 200
drawcircle C_{\_G6359}
color 0 0 0


% Constructing points P_{\_G6362} and P_{\_G6365} which are in intersection of C_{\_G6359} and k(I,P_{a})
intersec2 P_{\_G6362} P_{\_G6365} C_{\_G6359} k(I,P_{a}) 
cmark_r P_{\_G6362}
cmark_r P_{\_G6365}

% Constructing a line x1 which passes through point M_{a} and point P_{\_G6362}
line x1 M_{a} P_{\_G6362} 

color 200 200 200
drawline x1
color 0 0 0


% Constructing a line a which passes through point M_{a} and point P_{\_G6365}
line a M_{a} P_{\_G6365} 

color 200 200 200
drawline a
color 0 0 0



% NDG:  lines c and a are not parallel% DET:  lines c and a are not the same
% Constructing a point B which belongs to line c and line a
intersec B c a 
cmark_b B



% Constructing a point C such that M_{a}C/M_{a}B=-1
towards C M_{a} B -1 
cmark_b C
color 200 200 200
drawsegment B C 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  lines c and a are not parallel; point M_{a} is outside the circle k(I,P_{a}); point A is outside the circle k(I,P_{a}); points P_{a} and I are not the same; line h_{M_{a},-1/1}(AP`_{a}) and circle k_over(I,M_{a}) intersect; points I and M_{a} are not the same
% Determination conditions:  lines c and a are not the same; points M_{a} and I are not the same