Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point I 74.37 61.15
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_r E_{a}
cmark_b I
cmark_r N
color 0 0 0
fontsize 10

% DET:  points E_{a} and N are not the same
% Constructing a line m(H_{b}H_{c}) which passes through point E_{a} and point N
line m(H_{b}H_{c}) E_{a} N 

color 200 200 200
drawline m(H_{b}H_{c})
color 0 0 0



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

color 200 200 200
drawcircle k(N,M_{a})
color 0 0 0



% NDG:  line m(H_{b}H_{c}) and circle k(N,M_{a}) intersect% DET:  points E_{a} and M_{a} must be different
% Constructing a point M_{a} which is an image of the point E_{a} in the symmetry to point/line N
sim M_{a} N E_{a} 
cmark_b M_{a}


% 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_{\_G42047} of the segment IM_{a}
midpoint P_{\_G42047} I M_{a} 
cmark_r P_{\_G42047}

% Constructing a circle k_over(I,M_{a}) whose center is at point P_{\_G42047} and which passes through point I
circle k_over(I,M_{a}) P_{\_G42047} I 

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



% NDG:  point I is inside the circle k(N,M_{a}); points I and N are not the same
% Calculating distance V[_G42233] from point N to point E_{a}
distance V[_G42233] N E_{a} 


% Calculating distance V[_G42257] from point N to point I
distance V[_G42257] N I 


% Calculating value V[_G42278] using formula V[_G42233]/V[_G42257]
expression V[_G42278]  { V[_G42233]/V[_G42257]  } 


% Constructing a point P_{\_G42309} such that NP_{\_G42309}/NI=V[_G42233]/V[_G42257]
towards P_{\_G42309} N I V[_G42278] 
cmark_r P_{\_G42309}

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G42309}
circle k(I,P_{a}) I P_{\_G42309} 

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



% NDG:  circles k(I,P_{a}) and k_over(I,M_{a}) intersect% DET:  circles k(I,P_{a}) and k_over(I,M_{a}) are not the same
% Constructing points P_{a} and A_{fi} which are in intersection of k(I,P_{a}) and k_over(I,M_{a})
intersec2 P_{a} A_{fi} k(I,P_{a}) k_over(I,M_{a}) 
cmark_r P_{a}
cmark_r A_{fi}



% Constructing a point P`_{a} such that P_{a}P`_{a}/P_{a}M_{a}=2
towards P`_{a} P_{a} M_{a} 2 
cmark_r P`_{a}
color 200 200 200
drawsegment P_{a} P`_{a} 
color 0 0 0


% NDG:  point M_{a} is outside the circle k(I,P_{a})
% Constructing midpoint P_{\_G42914} of the segment M_{a}I
midpoint P_{\_G42914} M_{a} I 
cmark_r P_{\_G42914}

% Constructing a circle C_{\_G42917} whose center is at point P_{\_G42914} and which passes through point M_{a}
circle C_{\_G42917} P_{\_G42914} M_{a} 

color 200 200 200
drawcircle C_{\_G42917}
color 0 0 0


% Constructing points P_{\_G42920} and P_{\_G42923} which are in intersection of C_{\_G42917} and k(I,P_{a})
intersec2 P_{\_G42920} P_{\_G42923} C_{\_G42917} k(I,P_{a}) 
cmark_r P_{\_G42920}
cmark_r P_{\_G42923}

% Constructing a line x1 which passes through point M_{a} and point P_{\_G42920}
line x1 M_{a} P_{\_G42920} 

color 200 200 200
drawline x1
color 0 0 0


% Constructing a line a which passes through point M_{a} and point P_{\_G42923}
line a M_{a} P_{\_G42923} 

color 200 200 200
drawline a
color 0 0 0



% NDG:  line a and circle k(N,M_{a}) intersect% DET:  points M_{a} and H_{a} must be different
% Constructing a point P_{\_G43257} which is a foot of the point N on the line a
foot P_{\_G43257} N a 
cmark_r P_{\_G43257}
color 200 200 200
drawline N P_{\_G43257} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point M_{a} in the symmetry to point/line P_{\_G43257}
sim H_{a} P_{\_G43257} M_{a} 
cmark_b H_{a}


% DET:  points H_{a} and E_{a} are not the same
% Constructing a line h_{a} which passes through point H_{a} and point E_{a}
line h_{a} H_{a} E_{a} 

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




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

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




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

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



% NDG:  lines AP`_{a} and h_{a} are not parallel% DET:  lines AP`_{a} and h_{a} are not the same
% Constructing a point A which belongs to line AP`_{a} and line h_{a}
intersec A AP`_{a} h_{a} 
cmark_t A


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

color 200 200 200
drawline s_{a}
color 0 0 0



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


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

color 200 200 200
drawcircle k(N_{a},C)
color 0 0 0



% NDG:  line a and circle k(N_{a},C) intersect
% Constructing points C and B which are in intersection of k(N_{a},C) and a
intersec2 C B k(N_{a},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(N_{a},C) intersect; points I and N_{a} are not the same; lines m_{a} and s_{a} are not parallel; lines AP`_{a} and h_{a} are not parallel; line a and circle k(N,M_{a}) intersect; point M_{a} is outside the circle k(I,P_{a}); circles k(I,P_{a}) and k_over(I,M_{a}) intersect; point I is inside the circle k(N,M_{a}); points I and N are not the same; points I and M_{a} are not the same; line m(H_{b}H_{c}) and circle k(N,M_{a}) intersect; points E_{a} and N are not the same
% Determination conditions:  lines m_{a} and s_{a} are not the same; points I and A are not the same; lines AP`_{a} and h_{a} are not the same; points H_{a} and E_{a} are not the same; points M_{a} and H_{a} must be different; circles k(I,P_{a}) and k_over(I,M_{a}) are not the same; points M_{a} and I are not the same; points E_{a} and M_{a} must be different; points E_{a} and N are not the same