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Indonesia MO
2022 Indonesia MO
6
6
Part of
2022 Indonesia MO
Problems
(1)
GET WRECKED!
Source: Indonesia MO 2022/6
10/5/2022
In a triangle
A
B
C
ABC
A
BC
,
D
D
D
and
E
E
E
lies on
A
B
AB
A
B
and
A
C
AC
A
C
such that
D
E
DE
D
E
is parallel to
B
C
BC
BC
. There exists point
P
P
P
in the interior of
B
D
E
C
BDEC
B
D
EC
such that
∠
B
P
D
=
∠
C
P
E
=
9
0
∘
\angle BPD = \angle CPE = 90^{\circ}
∠
BP
D
=
∠
CPE
=
9
0
∘
Prove that the line
A
P
AP
A
P
passes through the circumcenter of triangles
E
P
D
EPD
EP
D
and
B
P
C
BPC
BPC
.
geometry