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National and Regional Contests
Indonesia Contests
Indonesia MO
2019 Indonesia MO
3
3
Part of
2019 Indonesia MO
Problems
(1)
INAMO 2019 P3
Source: INAMO 2019 P3
7/2/2019
Given that
A
B
C
D
ABCD
A
BC
D
is a rectangle such that
A
D
>
A
B
AD > AB
A
D
>
A
B
, where
E
E
E
is on
A
D
AD
A
D
such that
B
E
⊥
A
C
BE \perp AC
BE
⊥
A
C
. Let
M
M
M
be the intersection of
A
C
AC
A
C
and
B
E
BE
BE
. Let the circumcircle of
△
A
B
E
\triangle ABE
△
A
BE
intersects
A
C
AC
A
C
and
B
C
BC
BC
at
N
N
N
and
F
F
F
. Moreover, let the circumcircle of
△
D
N
E
\triangle DNE
△
D
NE
intersects
C
D
CD
C
D
at
G
G
G
. Suppose
F
G
FG
FG
intersects
A
B
AB
A
B
at
P
P
P
. Prove that
P
M
=
P
N
PM = PN
PM
=
PN
.
Inamo
geometry