Construction in GCLC language
dim 120 120
point M_{a} 65 40
point N 72.5 61.93
color 220 0 0
fontsize 11
cmark_b M_{a}
cmark_r N
color 0 0 0
fontsize 10
% point H_{a} is given by the problem setting, but it has to belong to the circle k(N,M_{a}) which is constructible from the others objects given
% 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
% Generating number V[_G124114] with value 0.8842473413941079
number V[_G124114] 0.8842473413941079
% Calculating value V[_G124135] using formula V[_G124114]*360
expression V[_G124135] { V[_G124114]*360 }
% Constructing a point H_{a} which is an image of the point V[_G124135] in a rotation around the point N for the angle M_{a}
rotate H_{a} N V[_G124135] M_{a}
color 220 0 0
fontsize 11
cmark_b H_{a}
color 0 0 0
fontsize 10
color 200 200 200
drawarc_p N M_{a} V[_G124135]
color 0 0 0
% DET: points H_{a} and M_{a} are not the same
% Constructing a line a which passes through point H_{a} and point M_{a}
line a H_{a} M_{a}
color 200 200 200
drawline 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}
% DET: points E_{a} and H_{a} are not the same
% Constructing a line h_{a} which passes through point E_{a} and point H_{a}
line h_{a} E_{a} H_{a}
color 200 200 200
drawline h_{a}
color 0 0 0
% Constructing a point A such that H_{a}A/H_{a}E_{a}=0.8842473413941079
towards A H_{a} E_{a} 0.8842473413941079
cmark_t A
color 200 200 200
drawsegment H_{a} E_{a}
color 0 0 0
% Constructing a line L_{\_G124582} which passes through point A and point M_{a}
line L_{\_G124582} A M_{a}
color 200 200 200
drawline L_{\_G124582}
color 0 0 0
% Constructing a point P_{\_G124683} with coordinates (0,0)
point P_{\_G124683} 0 0
cmark_r P_{\_G124683}
% Constructing a point P_{\_G124607} such that AP_{\_G124607}/AP_{\_G124683}=2
towards P_{\_G124607} A P_{\_G124683} 2
cmark_r P_{\_G124607}
color 200 200 200
drawsegment A P_{\_G124607}
color 0 0 0
% Constructing a point P_{\_G124652} such that AP_{\_G124652}/AP_{\_G124683}=3
towards P_{\_G124652} A P_{\_G124683} 3
cmark_r P_{\_G124652}
color 200 200 200
drawsegment A P_{\_G124652}
color 0 0 0
% Constructing a line L_{\_G124613} which passes through point M_{a} and point P_{\_G124652}
line L_{\_G124613} M_{a} P_{\_G124652}
color 200 200 200
drawline L_{\_G124613}
color 0 0 0
% Constructing a line L_{\_G124576} which contains the point P_{\_G124607} and is parallel to the line L_{\_G124613}
parallel L_{\_G124576} P_{\_G124607} L_{\_G124613}
color 200 200 200
drawline L_{\_G124576}
color 0 0 0
% Constructing a point G which belongs to line L_{\_G124576} and line L_{\_G124582}
intersec G L_{\_G124576} L_{\_G124582}
cmark_t G
% Constructing a point O such that NO/NG=3
towards O N G 3
cmark_t O
color 200 200 200
drawsegment N O
color 0 0 0
% NDG: points A and O are not the same
% Constructing a circle k(O,C) whose center is at point O and which passes through point A
circle k(O,C) O A
color 200 200 200
drawcircle k(O,C)
color 0 0 0
% NDG: line a and circle k(O,C) intersect
% Constructing points C and B which are in intersection of k(O,C) and a
intersec2 C B k(O,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(O,C) intersect; points A and O 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: points E_{a} and H_{a} are not the same; points M_{a} and E_{a} must be different; points H_{a} and M_{a} are not the same; points M_{a} and N are not the same