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Problems
Contests
National and Regional Contests
The Philippines Contests
Philippine MO
2018 Philippine MO
1
1
Part of
2018 Philippine MO
Problems
(1)
5AB = 4BC, <B = 60
Source: Philippines MO 2018/1
8/4/2018
In triangle
A
B
C
ABC
A
BC
with
∠
A
B
C
=
6
0
∘
\angle ABC = 60^{\circ}
∠
A
BC
=
6
0
∘
and
5
A
B
=
4
B
C
5AB = 4BC
5
A
B
=
4
BC
, points
D
D
D
and
E
E
E
are the feet of the altitudes from
B
B
B
and
C
C
C
, respectively.
M
M
M
is the midpoint of
B
D
BD
B
D
and the circumcircle of triangle
B
M
C
BMC
BMC
meets line
A
C
AC
A
C
again at
N
N
N
. Lines
B
N
BN
BN
and
C
M
CM
CM
meet at
P
P
P
. Prove that
∠
E
D
P
=
9
0
∘
\angle EDP = 90^{\circ}
∠
E
D
P
=
9
0
∘
.
geometry