Construction in GCLC language

dim 120 120

point H_{a} 80 40
point I 74.37 61.15
point N 72.5 61.93

color 220 0 0
fontsize 11

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

% NDG:  points H_{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 H_{a}
circle k(N,M_{a}) N H_{a} 

color 200 200 200
drawcircle k(N,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[_G74786] from point N to point H_{a}
distance V[_G74786] N H_{a} 


% Calculating distance V[_G74810] from point N to point I
distance V[_G74810] N I 


% Calculating value V[_G74831] using formula V[_G74786]/V[_G74810]
expression V[_G74831]  { V[_G74786]/V[_G74810]  } 


% Constructing a point P_{\_G74862} such that NP_{\_G74862}/NI=V[_G74786]/V[_G74810]
towards P_{\_G74862} N I V[_G74831] 
cmark_r P_{\_G74862}

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G74862}
circle k(I,P_{a}) I P_{\_G74862} 

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



% NDG:  point H_{a} is outside the circle k(I,P_{a})
% Constructing midpoint P_{\_G75235} of the segment H_{a}I
midpoint P_{\_G75235} H_{a} I 
cmark_r P_{\_G75235}

% Constructing a circle C_{\_G75238} whose center is at point P_{\_G75235} and which passes through point H_{a}
circle C_{\_G75238} P_{\_G75235} H_{a} 

color 200 200 200
drawcircle C_{\_G75238}
color 0 0 0


% Constructing points P_{\_G75241} and P_{\_G75244} which are in intersection of C_{\_G75238} and k(I,P_{a})
intersec2 P_{\_G75241} P_{\_G75244} C_{\_G75238} k(I,P_{a}) 
cmark_r P_{\_G75241}
cmark_r P_{\_G75244}

% Constructing a line y1 which passes through point H_{a} and point P_{\_G75241}
line y1 H_{a} P_{\_G75241} 

color 200 200 200
drawline y1
color 0 0 0


% Constructing a line a which passes through point H_{a} and point P_{\_G75244}
line a H_{a} P_{\_G75244} 

color 200 200 200
drawline a
color 0 0 0



% NDG:  line a and circle k(N,M_{a}) intersect% DET:  points H_{a} and M_{a} must be different
% Constructing a point P_{\_G75578} which is a foot of the point N on the line a
foot P_{\_G75578} N a 
cmark_r P_{\_G75578}
color 200 200 200
drawline N P_{\_G75578} 
color 0 0 0

% Constructing a point M_{a} which is an image of the point H_{a} in the symmetry to point/line P_{\_G75578}
sim M_{a} P_{\_G75578} H_{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



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

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



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


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

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



% NDG:  points I and M_{a} are not the same
% Constructing midpoint P_{\_G76046} of the segment IM_{a}
midpoint P_{\_G76046} I M_{a} 
cmark_r P_{\_G76046}

% Constructing a circle k_over(I,M_{a}) whose center is at point P_{\_G76046} and which passes through point I
circle k_over(I,M_{a}) P_{\_G76046} I 

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



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



% 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



% 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; circles k_over(I,M_{a}) and k(I,P_{a}) intersect; points I and M_{a} are not the same; line m(H_{b}H_{c}) and circle k(N,M_{a}) intersect; line a and circle k(N,M_{a}) intersect; point H_{a} is outside the circle k(I,P_{a}); point I is inside the circle k(N,M_{a}); points I and N are not the same; points H_{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; circles k_over(I,M_{a}) and k(I,P_{a}) are not the same; points E_{a} and H_{a} are not the same; points M_{a} and E_{a} must be different; points N and M_{a} are not the same; points M_{a} and I are not the same; points H_{a} and M_{a} must be different