Construction in GCLC language
dim 120 120
point H_{a} 80 40
point H_{c} 68.91 84.83
point T_{a} 70.86 40
color 220 0 0
fontsize 11
cmark_b H_{a}
cmark_lt H_{c}
cmark_b T_{a}
color 0 0 0
fontsize 10
% DET: points H_{a} and H_{c} are not the same
% Constructing a line H_{c}H_{a} which passes through point H_{a} and point H_{c}
line H_{c}H_{a} H_{a} H_{c}
color 200 200 200
drawline H_{c}H_{a}
color 0 0 0
% DET: points H_{a} and T_{a} are not the same
% Constructing a line a which passes through point H_{a} and point T_{a}
line a H_{a} T_{a}
color 200 200 200
drawline a
color 0 0 0
% Constructing a line h_{a} which is perpendicular to line a and which passes through point H_{a}
perp h_{a} H_{a} a
color 200 200 200
drawline h_{a}
color 0 0 0
% NDG: points H_{a} and T_{a} are not the same; points H_{c} and H_{a} are not the same% DET: points H_{a} and T_{a} are not the same
% Constructing an angle V[_G107099] which is equal to the angle H_{c}H_{a}T_{a}
angle_o V[_G107099] H_{c} H_{a} T_{a}
% Calculating value angle[_G107178] using formula 1/pow(2,0)*V[_G107099]+0/pow(2,0)*180
expression angle[_G107178] { 1/pow(2,0)*V[_G107099]+0/pow(2,0)*180 }
% Constructing a point P_{\_G107175} which is an image of the point T_{a} in a rotation around the point H_{a} for the angle 1/pow(2,0)*V[_G107099]+0/pow(2,0)*180
rotate P_{\_G107175} H_{a} angle[_G107178] T_{a}
cmark_r P_{\_G107175}
color 200 200 200
drawarc_p H_{a} T_{a} angle[_G107178]
color 0 0 0
% Constructing a line H_{a}H_{b} which passes through point H_{a} and point P_{\_G107175}
line H_{a}H_{b} H_{a} P_{\_G107175}
color 200 200 200
drawline H_{a}H_{b}
color 0 0 0
% NDG: points H_{c} and H_{a} are not the same; points H_{a} and T_{a} are not the same; points T_{a} and H_{c} are not the same
% Constructing an angle angle[_G107661] which is equal to the angle H_{c}H_{a}T_{a}
angle_o angle[_G107661] H_{c} H_{a} T_{a}
% Calculating value angle[_G107673] using formula 90-(1/pow(2,1)*angle[_G107661]+0/pow(2,0)*180)
expression angle[_G107673] { 90-(1/pow(2,1)*angle[_G107661]+0/pow(2,0)*180) }
% Constructing a line L_{\_G107744} which passes through point T_{a} and point H_{c}
line L_{\_G107744} T_{a} H_{c}
color 200 200 200
drawline L_{\_G107744}
color 0 0 0
% Constructing bisector L_{\_G107747} of the segment T_{a}H_{c}
med L_{\_G107747} T_{a} H_{c}
color 200 200 200
drawline L_{\_G107747}
color 0 0 0
color 200 200 200
drawsegment T_{a} H_{c}
color 0 0 0
% Constructing a point P_{\_G107750} which is an image of the point H_{c} in a rotation around the point T_{a} for the angle angle[_G107673]
rotate P_{\_G107750} T_{a} angle[_G107673] H_{c}
cmark_r P_{\_G107750}
color 200 200 200
drawarc_p T_{a} H_{c} angle[_G107673]
color 0 0 0
% Constructing a line L_{\_G107753} which passes through point T_{a} and point P_{\_G107750}
line L_{\_G107753} T_{a} P_{\_G107750}
color 200 200 200
drawline L_{\_G107753}
color 0 0 0
% Constructing a point P_{\_G107756} which belongs to line L_{\_G107747} and line L_{\_G107753}
intersec P_{\_G107756} L_{\_G107747} L_{\_G107753}
cmark_r P_{\_G107756}
% Constructing a circle circle[T_{a},H_{c},angle[c][s[a]]] whose center is at point P_{\_G107756} and which passes through point T_{a}
circle circle[T_{a},H_{c},angle[c][s[a]]] P_{\_G107756} T_{a}
color 200 200 200
drawcircle circle[T_{a},H_{c},angle[c][s[a]]]
color 0 0 0
% NDG: line h_{a} and circle circle[T_{a},H_{c},angle[c][s[a]]] intersect
% Constructing points A_{ca2} and A which are in intersection of circle[T_{a},H_{c},angle[c][s[a]]] and h_{a}
intersec2 A_{ca2} A circle[T_{a},H_{c},angle[c][s[a]]] h_{a}
cmark_r A_{ca2}
cmark_t A
% DET: points A and H_{c} are not the same
% Constructing a line c which passes through point A and point H_{c}
line c A H_{c}
color 200 200 200
drawline c
color 0 0 0
% NDG: lines a and c are not parallel% DET: lines a and c are not the same
% Constructing a point B which belongs to line a and line c
intersec B a c
cmark_b B
% Constructing a point M_{c} such that BM_{c}/BA=0.5
towards M_{c} B A 0.5
cmark_lt M_{c}
color 200 200 200
drawsegment B A
color 0 0 0
% NDG: points H_{a} and M_{c} are not the same
% Constructing a circle k(M_{c},A) whose center is at point M_{c} and which passes through point H_{a}
circle k(M_{c},A) M_{c} H_{a}
color 200 200 200
drawcircle k(M_{c},A)
color 0 0 0
% NDG: line H_{a}H_{b} and circle k(M_{c},A) intersect% DET: points H_{a} and H_{b} must be different
% Constructing a point P_{\_G109261} which is a foot of the point M_{c} on the line H_{a}H_{b}
foot P_{\_G109261} M_{c} H_{a}H_{b}
cmark_r P_{\_G109261}
color 200 200 200
drawline M_{c} P_{\_G109261}
color 0 0 0
% Constructing a point H_{b} which is an image of the point H_{a} in the symmetry to point/line P_{\_G109261}
sim H_{b} P_{\_G109261} H_{a}
cmark_rt H_{b}
% DET: points A and H_{b} are not the same
% Constructing a line b which passes through point A and point H_{b}
line b A H_{b}
color 200 200 200
drawline b
color 0 0 0
% NDG: lines a and b are not parallel% DET: lines a and b are not the same
% Constructing a point C which belongs to line a and line b
intersec C a b
cmark_b C
drawsegment A B
drawsegment A C
drawsegment B C
% Non-degenerate conditions: lines a and b are not parallel; line H_{a}H_{b} and circle k(M_{c},A) intersect; points H_{a} and M_{c} are not the same; lines a and c are not parallel; line h_{a} and circle circle[T_{a},H_{c},angle[c][s[a]]] intersect; points H_{c} and H_{a} are not the same; points H_{a} and T_{a} are not the same; points T_{a} and H_{c} are not the same; points H_{a} and T_{a} are not the same; points H_{c} and H_{a} are not the same
% Determination conditions: lines a and b are not the same; points A and H_{b} are not the same; points H_{a} and H_{b} must be different; lines a and c are not the same; points A and H_{c} are not the same; points H_{a} and T_{a} are not the same; points H_{a} and T_{a} are not the same; points H_{a} and H_{c} are not the same