Construction in GCLC language

dim 120 120

point E_{b} 50 56.36
point I 74.37 61.15
point M_{b} 95 67.5

color 220 0 0
fontsize 11

cmark_r E_{b}
cmark_b I
cmark_rt M_{b}
color 0 0 0
fontsize 10

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

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



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

color 200 200 200
drawline IM_{b}
color 0 0 0



% NDG:  points I and M_{b} are not the same
% Constructing midpoint P_{\_G52010} of the segment IM_{b}
midpoint P_{\_G52010} I M_{b} 
cmark_r P_{\_G52010}

% Constructing a circle k_over(I,M_{b}) whose center is at point P_{\_G52010} and which passes through point I
circle k_over(I,M_{b}) P_{\_G52010} I 

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



% DET:  points E_{b} and M_{b} are not the same
% Constructing bisector m(E_{b}M_{b}) of the segment E_{b}M_{b}
med m(E_{b}M_{b}) E_{b} M_{b} 

color 200 200 200
drawline m(E_{b}M_{b})
color 0 0 0

color 200 200 200
drawsegment E_{b} M_{b} 
color 0 0 0


% NDG:  lines m(E_{b}M_{b}) and m(H_{a}H_{c}) are not parallel% DET:  lines m(E_{b}M_{b}) and m(H_{a}H_{c}) are not the same
% Constructing a point N which belongs to line m(E_{b}M_{b}) and line m(H_{a}H_{c})
intersec N m(E_{b}M_{b}) m(H_{a}H_{c}) 
cmark_r N


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

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[_G52565] from point N to point E_{b}
distance V[_G52565] N E_{b} 


% Calculating distance V[_G52589] from point N to point I
distance V[_G52589] N I 


% Calculating value V[_G52610] using formula V[_G52565]/V[_G52589]
expression V[_G52610]  { V[_G52565]/V[_G52589]  } 


% Constructing a point P_{\_G52641} such that NP_{\_G52641}/NI=V[_G52565]/V[_G52589]
towards P_{\_G52641} N I V[_G52610] 
cmark_r P_{\_G52641}

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G52641}
circle k(I,P_{a}) I P_{\_G52641} 

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



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



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


% NDG:  point M_{b} is outside the circle k(I,P_{a})
% Constructing midpoint P_{\_G53246} of the segment M_{b}I
midpoint P_{\_G53246} M_{b} I 
cmark_r P_{\_G53246}

% Constructing a circle C_{\_G53249} whose center is at point P_{\_G53246} and which passes through point M_{b}
circle C_{\_G53249} P_{\_G53246} M_{b} 

color 200 200 200
drawcircle C_{\_G53249}
color 0 0 0


% Constructing points P_{\_G53252} and P_{\_G53255} which are in intersection of C_{\_G53249} and k(I,P_{a})
intersec2 P_{\_G53252} P_{\_G53255} C_{\_G53249} k(I,P_{a}) 
cmark_r P_{\_G53252}
cmark_r P_{\_G53255}

% Constructing a line x2 which passes through point M_{b} and point P_{\_G53252}
line x2 M_{b} P_{\_G53252} 

color 200 200 200
drawline x2
color 0 0 0


% Constructing a line b which passes through point M_{b} and point P_{\_G53255}
line b M_{b} P_{\_G53255} 

color 200 200 200
drawline b
color 0 0 0



% NDG:  line b and circle k(N,M_{a}) intersect% DET:  points M_{b} and H_{b} must be different
% Constructing a point P_{\_G53589} which is a foot of the point N on the line b
foot P_{\_G53589} N b 
cmark_r P_{\_G53589}
color 200 200 200
drawline N P_{\_G53589} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point M_{b} in the symmetry to point/line P_{\_G53589}
sim H_{b} P_{\_G53589} M_{b} 
cmark_rt H_{b}


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

color 200 200 200
drawline h_{b}
color 0 0 0




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

color 200 200 200
drawline m_{b}
color 0 0 0




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

color 200 200 200
drawline BP`_{b}
color 0 0 0



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


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

color 200 200 200
drawline s_{b}
color 0 0 0



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


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

color 200 200 200
drawcircle k(N_{b},A)
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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