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Slovenia Team Selection Tests
2019 Slovenia Team Selection Test
5
5
Part of
2019 Slovenia Team Selection Test
Problems
(1)
Slovenia 2019 TST1 P5
Source: 2019 Slovenia 1st TST Problem 5
2/19/2019
Let
A
B
C
ABC
A
BC
be a triangle and
D
,
E
D, E
D
,
E
and
F
F
F
the foots of heights from
A
,
B
A, B
A
,
B
and
C
C
C
respectively. Let
D
1
D_1
D
1
be such a point on
E
F
EF
EF
, that
D
F
=
D
1
E
DF = D_1 E
D
F
=
D
1
E
where
E
E
E
is between
D
1
D_1
D
1
and
F
F
F
. Similarly, let
D
2
D_2
D
2
be such a point on
E
F
EF
EF
, that
D
E
=
D
2
F
DE = D_2 F
D
E
=
D
2
F
where
F
F
F
is between
E
E
E
and
D
2
D_2
D
2
. Let the bisector of
D
D
1
DD_1
D
D
1
intersect
A
B
AB
A
B
at
P
P
P
and let the bisector of
D
D
2
DD_2
D
D
2
intersect
A
C
AC
A
C
at
Q
Q
Q
. Prove that,
P
Q
PQ
PQ
bisects
B
C
BC
BC
.
TST
geometry