Construction in GCLC language

dim 120 120

point I 74.37 61.15
point M_{c} 50 67.5
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_b I
cmark_lt M_{c}
cmark_r N
color 0 0 0
fontsize 10

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

color 200 200 200
drawline IM_{c}
color 0 0 0



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

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



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

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



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


% NDG:  points I and M_{c} are not the same
% Constructing midpoint P_{\_G53107} of the segment IM_{c}
midpoint P_{\_G53107} I M_{c} 
cmark_r P_{\_G53107}

% Constructing a circle k_over(I,M_{c}) whose center is at point P_{\_G53107} and which passes through point I
circle k_over(I,M_{c}) P_{\_G53107} I 

color 200 200 200
drawcircle k_over(I,M_{c})
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[_G53293] from point N to point M_{c}
distance V[_G53293] N M_{c} 


% Calculating distance V[_G53317] from point N to point I
distance V[_G53317] N I 


% Calculating value V[_G53338] using formula V[_G53293]/V[_G53317]
expression V[_G53338]  { V[_G53293]/V[_G53317]  } 


% Constructing a point P_{\_G53369} such that NP_{\_G53369}/NI=V[_G53293]/V[_G53317]
towards P_{\_G53369} N I V[_G53338] 
cmark_r P_{\_G53369}

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G53369}
circle k(I,P_{a}) I P_{\_G53369} 

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



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



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


% NDG:  point M_{c} is outside the circle k(I,P_{a})
% Constructing midpoint P_{\_G53974} of the segment M_{c}I
midpoint P_{\_G53974} M_{c} I 
cmark_r P_{\_G53974}

% Constructing a circle C_{\_G53977} whose center is at point P_{\_G53974} and which passes through point M_{c}
circle C_{\_G53977} P_{\_G53974} M_{c} 

color 200 200 200
drawcircle C_{\_G53977}
color 0 0 0


% Constructing points P_{\_G53980} and P_{\_G53983} which are in intersection of C_{\_G53977} and k(I,P_{a})
intersec2 P_{\_G53980} P_{\_G53983} C_{\_G53977} k(I,P_{a}) 
cmark_r P_{\_G53980}
cmark_r P_{\_G53983}

% Constructing a line x3 which passes through point M_{c} and point P_{\_G53980}
line x3 M_{c} P_{\_G53980} 

color 200 200 200
drawline x3
color 0 0 0


% Constructing a line c which passes through point M_{c} and point P_{\_G53983}
line c M_{c} P_{\_G53983} 

color 200 200 200
drawline c
color 0 0 0



% NDG:  line c and circle k(N,M_{a}) intersect% DET:  points M_{c} and H_{c} must be different
% Constructing a point P_{\_G54317} which is a foot of the point N on the line c
foot P_{\_G54317} N c 
cmark_r P_{\_G54317}
color 200 200 200
drawline N P_{\_G54317} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point M_{c} in the symmetry to point/line P_{\_G54317}
sim H_{c} P_{\_G54317} M_{c} 
cmark_lt H_{c}


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

color 200 200 200
drawline h_{c}
color 0 0 0




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

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




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

color 200 200 200
drawline CP`_{c}
color 0 0 0



% NDG:  lines CP`_{c} and h_{c} are not parallel% DET:  lines CP`_{c} and h_{c} are not the same
% Constructing a point C which belongs to line CP`_{c} and line h_{c}
intersec C CP`_{c} h_{c} 
cmark_b C


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

color 200 200 200
drawline s_{c}
color 0 0 0



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


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

color 200 200 200
drawcircle k(N_{c},B)
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  line c and circle k(N_{c},B) intersect; points I and N_{c} are not the same; lines m_{c} and s_{c} are not parallel; lines CP`_{c} and h_{c} are not parallel; line c and circle k(N,M_{a}) intersect; point M_{c} is outside the circle k(I,P_{a}); circles k(I,P_{a}) and k_over(I,M_{c}) intersect; point I is inside the circle k(N,M_{a}); points I and N are not the same; points I and M_{c} are not the same; line m(H_{b}H_{a}) and circle k(N,M_{a}) intersect; points M_{c} and N are not the same
% Determination conditions:  lines m_{c} and s_{c} are not the same; points I and C are not the same; lines CP`_{c} and h_{c} are not the same; points H_{c} and E_{c} are not the same; points M_{c} and H_{c} must be different; circles k(I,P_{a}) and k_over(I,M_{c}) are not the same; points M_{c} and E_{c} must be different; points M_{c} and N are not the same; points I and M_{c} are not the same