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Netherlands Contests
Dutch Mathematical Olympiad
1979 Dutch Mathematical Olympiad
4
4
Part of
1979 Dutch Mathematical Olympiad
Problems
(1)
3 parallel lines, symmetric points wrt angle bisectors
Source: Netherlands - Dutch NMO 1979 p4
1/28/2023
Given is the non-equilateral triangle
A
1
A
2
A
3
A_1A_2A_3
A
1
A
2
A
3
.
B
i
j
B_{ij}
B
ij
is the symmetric of
A
i
A_i
A
i
wrt the inner bisector of
∠
A
j
\angle A_j
∠
A
j
. Prove that lines
B
12
B
21
B_{12}B_{21}
B
12
B
21
,
B
13
B
31
B_{13}B_{31}
B
13
B
31
and
B
23
B
32
B_{23}B_{32}
B
23
B
32
are parallel.
geometry
parallel
symmetry
angle bisector