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Baltic Way
2017 Baltic Way
14
14
Part of
2017 Baltic Way
Problems
(1)
Lots of perpendiculars
Source: Baltic Way 2017 Problem 14
11/11/2017
Let
P
P
P
be a point inside the acute angle
∠
B
A
C
\angle BAC
∠
B
A
C
. Suppose that
∠
A
B
P
=
∠
A
C
P
=
9
0
∘
\angle ABP = \angle ACP = 90^{\circ}
∠
A
BP
=
∠
A
CP
=
9
0
∘
. The points
D
D
D
and
E
E
E
are on the segments
B
A
BA
B
A
and
C
A
CA
C
A
, respectively, such that
B
D
=
B
P
BD = BP
B
D
=
BP
and
C
P
=
C
E
CP = CE
CP
=
CE
. The points
F
F
F
and
G
G
G
are on the segments
A
C
AC
A
C
and
A
B
AB
A
B
, respectively, such that
D
F
DF
D
F
is perpendicular to
A
B
AB
A
B
and
E
G
EG
EG
is perpendicular to
A
C
AC
A
C
. Show that
P
F
=
P
G
PF = PG
PF
=
PG
.
geometry