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National and Regional Contests
Belarus Contests
Belarus Team Selection Test
2019 Belarus Team Selection Test
5.2
5.2
Part of
2019 Belarus Team Selection Test
Problems
(1)
Moving points and lines
Source: 2019 Belarus Team Selection Test 5.2
9/2/2019
Let
A
A
1
AA_1
A
A
1
be the bisector of a triangle
A
B
C
ABC
A
BC
. Points
D
D
D
and
F
F
F
are chosen on the line
B
C
BC
BC
such that
A
1
A_1
A
1
is the midpoint of the segment
D
F
DF
D
F
. A line
l
l
l
, different from
B
C
BC
BC
, passes through
A
1
A_1
A
1
and intersects the lines
A
B
AB
A
B
and
A
C
AC
A
C
at points
B
1
B_1
B
1
and
C
1
C_1
C
1
, respectively. Find the locus of the points of intersection of the lines
B
1
D
B_1D
B
1
D
and
C
1
F
C_1F
C
1
F
for all possible positions of
l
l
l
.(M. Karpuk)
geometry
moving points