Construction in GCLC language

dim 120 120

point M_{b} 95 67.5
point H_{c} 68.91 84.83

color 220 0 0
fontsize 11

cmark_rt M_{b}
cmark_lt H_{c}
color 0 0 0
fontsize 10


% point H_{a} is given by the problem setting, but it has to belong to the circle k(M_{b},C) which is constructible from the others objects given 
% NDG:  points H_{c} and M_{b} are not the same
% Constructing a circle k(M_{b},C) whose center is at point M_{b} and which passes through point H_{c}
circle k(M_{b},C) M_{b} H_{c} 

color 200 200 200
drawcircle k(M_{b},C)
color 0 0 0




% Generating number V[_G57259] with value 0.9658693097286719
number V[_G57259] 0.9658693097286719 


% Calculating value V[_G57280] using formula V[_G57259]*360
expression V[_G57280]  { V[_G57259]*360  } 


% Constructing a point H_{a} which is an image of the point V[_G57280] in a rotation around the point M_{b} for the angle H_{c}
rotate H_{a} M_{b} V[_G57280] H_{c} 
color 220 0 0
fontsize 11
cmark_b H_{a}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p M_{b} H_{c} V[_G57280] 
color 0 0 0


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

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

color 200 200 200
drawsegment H_{a} M_{b} 
color 0 0 0


% DET:  points H_{a} and H_{c} are not the same
% Constructing bisector m(H_{a}H_{c}) of the segment H_{a}H_{c}
med m(H_{a}H_{c}) H_{a} H_{c} 

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

color 200 200 200
drawsegment H_{a} H_{c} 
color 0 0 0


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



% Generating number V[_G57919] with value 0.9658693097286719
number V[_G57919] 0.9658693097286719 


% Calculating value V[_G57940] using formula V[_G57919]*360
expression V[_G57940]  { V[_G57919]*360  } 


% Constructing a point A which is an image of the point V[_G57940] in a rotation around the point M_{b} for the angle H_{a}
rotate A M_{b} V[_G57940] H_{a} 
cmark_t A
color 200 200 200
drawarc_p M_{b} H_{a} V[_G57940] 
color 0 0 0



% Constructing a point C such that AC/AM_{b}=2
towards C A M_{b} 2 
cmark_b C
color 200 200 200
drawsegment A C 
color 0 0 0


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

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



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

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



% NDG:  lines h_{a} and h_{c} are not parallel% DET:  lines h_{a} and h_{c} are not the same
% Constructing a point H which belongs to line h_{a} and line h_{c}
intersec H h_{a} h_{c} 
cmark_rt H



% Constructing a line L_{\_G58351} which passes through point N and point H
line L_{\_G58351} N H 

color 200 200 200
drawline L_{\_G58351}
color 0 0 0


% Constructing a point P_{\_G58452} with coordinates (0,0)
point P_{\_G58452} 0 0 
cmark_r P_{\_G58452}

% Constructing a point P_{\_G58376} such that NP_{\_G58376}/NP_{\_G58452}=-1
towards P_{\_G58376} N P_{\_G58452} -1 
cmark_r P_{\_G58376}
color 200 200 200
drawsegment P_{\_G58452} P_{\_G58376} 
color 0 0 0

% Constructing a point P_{\_G58421} such that NP_{\_G58421}/NP_{\_G58452}=3
towards P_{\_G58421} N P_{\_G58452} 3 
cmark_r P_{\_G58421}
color 200 200 200
drawsegment N P_{\_G58421} 
color 0 0 0

% Constructing a line L_{\_G58382} which passes through point H and point P_{\_G58421}
line L_{\_G58382} H P_{\_G58421} 

color 200 200 200
drawline L_{\_G58382}
color 0 0 0


% Constructing a line L_{\_G58345} which contains the point P_{\_G58376} and is parallel to the line L_{\_G58382}
parallel L_{\_G58345} P_{\_G58376} L_{\_G58382} 

color 200 200 200
drawline L_{\_G58345}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G58345} and line L_{\_G58351}
intersec G L_{\_G58345} L_{\_G58351} 
cmark_t G



% Constructing a point B such that M_{b}B/M_{b}G=3
towards B M_{b} G 3 
cmark_b B
color 200 200 200
drawsegment M_{b} B 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  lines h_{a} and h_{c} are not parallel; lines m(H_{a}H_{c}) and m(H_{a}M_{b}) are not parallel; points H_{c} and M_{b} are not the same
% Determination conditions:  lines h_{a} and h_{c} are not the same; points H_{c} and C are not the same; points A and H_{a} are not the same; lines m(H_{a}H_{c}) and m(H_{a}M_{b}) are not the same; points H_{a} and H_{c} are not the same; points H_{a} and M_{b} are not the same