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2023 ISL
G1
G1
Part of
2023 ISL
Problems
(1)
this hAOpefully shoudn't BE weird
Source: 2023 IMO Shortlist G1
7/17/2024
Let
A
B
C
D
E
ABCDE
A
BC
D
E
be a convex pentagon such that
∠
A
B
C
=
∠
A
E
D
=
9
0
∘
\angle ABC = \angle AED = 90^\circ
∠
A
BC
=
∠
A
E
D
=
9
0
∘
. Suppose that the midpoint of
C
D
CD
C
D
is the circumcenter of triangle
A
B
E
ABE
A
BE
. Let
O
O
O
be the circumcenter of triangle
A
C
D
ACD
A
C
D
.Prove that line
A
O
AO
A
O
passes through the midpoint of segment
B
E
BE
BE
.
IMO Shortlist
geometry