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Poland - Second Round
1979 Poland - Second Round
4
4
Part of
1979 Poland - Second Round
Problems
(1)
lines after symmetry of plane wrt line k
Source: Polish MO Recond Round 1979 p4
9/9/2024
Let
S
k
S_k
S
k
be the symmetry of the plane with respect to the line
k
k
k
. Prove that equality holds for every lines
a
,
b
,
c
a, b, c
a
,
b
,
c
contained in one plane
S
a
S
b
S
c
S
a
S
b
S
c
S
b
S
c
S
a
S
b
S
c
S
a
=
S
b
S
c
S
a
S
b
S
c
S
a
S
a
S
b
S
c
S
a
S
b
S
c
S_aS_bS_cS_aS_bS_cS_bS_cS_aS_bS_cS_a = S_bS_cS_aS_bS_cS_aS_aS_bS_cS_aS_bS_c
S
a
S
b
S
c
S
a
S
b
S
c
S
b
S
c
S
a
S
b
S
c
S
a
=
S
b
S
c
S
a
S
b
S
c
S
a
S
a
S
b
S
c
S
a
S
b
S
c
geometry
symmetry
3D geometry
lines