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National and Regional Contests
Bosnia Herzegovina Contests
Bosnia Herzegovina Team Selection Test
2018 Bosnia and Herzegovina Team Selection Test
1
1
Part of
2018 Bosnia and Herzegovina Team Selection Test
Problems
(1)
Bosnia and Herzegovina 2018 TST Day 1 Problem 1
Source: Bosnia and Herzegovina 2018 TST
9/15/2018
In acute triangle
A
B
C
ABC
A
BC
(
A
B
<
A
C
)
(AB < AC)
(
A
B
<
A
C
)
let
D
D
D
,
E
E
E
and
F
F
F
be foots of perpedicular from
A
A
A
,
B
B
B
and
C
C
C
to
B
C
BC
BC
,
C
A
CA
C
A
and
A
B
AB
A
B
, respectively. Let
P
P
P
and
Q
Q
Q
be points on line
E
F
EF
EF
such that
D
P
⊥
E
F
DP \perp EF
D
P
⊥
EF
and
B
Q
=
C
Q
BQ=CQ
BQ
=
CQ
. Prove that
∠
A
D
P
=
∠
P
B
Q
\angle ADP = \angle PBQ
∠
A
D
P
=
∠
PBQ
geometry
perpendicular
orthocenter