Construction in GCLC language

dim 120 120

point I 74.37 61.15
point M_{a} 65 40
point N 72.5 61.93

color 220 0 0
fontsize 11

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

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

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



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

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



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


% NDG:  points I and M_{a} are not the same
% Constructing midpoint P_{\_G81461} of the segment IM_{a}
midpoint P_{\_G81461} I M_{a} 
cmark_r P_{\_G81461}

% Constructing a circle k_over(I,M_{a}) whose center is at point P_{\_G81461} and which passes through point I
circle k_over(I,M_{a}) P_{\_G81461} 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[_G81647] from point N to point M_{a}
distance V[_G81647] N M_{a} 


% Calculating distance V[_G81671] from point N to point I
distance V[_G81671] N I 


% Calculating value V[_G81692] using formula V[_G81647]/V[_G81671]
expression V[_G81692]  { V[_G81647]/V[_G81671]  } 


% Constructing a point P_{\_G81723} such that NP_{\_G81723}/NI=V[_G81647]/V[_G81671]
towards P_{\_G81723} N I V[_G81692] 
cmark_r P_{\_G81723}

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G81723}
circle k(I,P_{a}) I P_{\_G81723} 

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_{\_G82328} of the segment M_{a}I
midpoint P_{\_G82328} M_{a} I 
cmark_r P_{\_G82328}

% Constructing a circle C_{\_G82331} whose center is at point P_{\_G82328} and which passes through point M_{a}
circle C_{\_G82331} P_{\_G82328} M_{a} 

color 200 200 200
drawcircle C_{\_G82331}
color 0 0 0


% Constructing points P_{\_G82334} and P_{\_G82337} which are in intersection of C_{\_G82331} and k(I,P_{a})
intersec2 P_{\_G82334} P_{\_G82337} C_{\_G82331} k(I,P_{a}) 
cmark_r P_{\_G82334}
cmark_r P_{\_G82337}

% Constructing a line x1 which passes through point M_{a} and point P_{\_G82334}
line x1 M_{a} P_{\_G82334} 

color 200 200 200
drawline x1
color 0 0 0


% Constructing a line a which passes through point M_{a} and point P_{\_G82337}
line a M_{a} P_{\_G82337} 

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_{\_G82671} which is a foot of the point N on the line a
foot P_{\_G82671} N a 
cmark_r P_{\_G82671}
color 200 200 200
drawline N P_{\_G82671} 
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_{\_G82671}
sim H_{a} P_{\_G82671} 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 M_{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 E_{a} must be different; points M_{a} and N are not the same; points I and M_{a} are not the same