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Contests
National and Regional Contests
Malaysia Contests
Malaysian IMO Training Camp
BIMO 2022
6
6
Part of
BIMO 2022
Problems
(1)
FX and BZ meet at w
Source: Own. Malaysian IMO TST 2022 P6
5/13/2022
Given a triangle
A
B
C
ABC
A
BC
with
A
B
=
A
C
AB=AC
A
B
=
A
C
and circumcenter
O
O
O
. Let
D
D
D
and
E
E
E
be midpoints of
A
C
AC
A
C
and
A
B
AB
A
B
respectively, and let
D
E
DE
D
E
intersect
A
O
AO
A
O
at
F
F
F
. Denote
ω
\omega
ω
to be the circle
(
B
O
E
)
(BOE)
(
BOE
)
. Let
B
D
BD
B
D
intersect
ω
\omega
ω
again at
X
X
X
and let
A
X
AX
A
X
intersect
ω
\omega
ω
again at
Y
Y
Y
. Suppose the line parallel to
A
B
AB
A
B
passing through
O
O
O
meets
C
Y
CY
C
Y
at
Z
Z
Z
. Prove that the lines
F
X
FX
FX
and
B
Z
BZ
BZ
meet at
ω
\omega
ω
.Proposed by Ivan Chan Kai Chin
geometry