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Benelux
2021 Benelux
3
3
Part of
2021 Benelux
Problems
(1)
Circumcentre on perpendicular bisector (BxMO2021 P3)
Source: BxMO2021 problem 3
5/3/2021
A cyclic quadrilateral
A
B
X
C
ABXC
A
BXC
has circumcentre
O
O
O
. Let
D
D
D
be a point on line
B
X
BX
BX
such that
A
D
=
B
D
AD = BD
A
D
=
B
D
. Let
E
E
E
be a point on line
C
X
CX
CX
such that
A
E
=
C
E
AE = CE
A
E
=
CE
. Prove that the circumcentre of triangle
△
D
E
X
\triangle DEX
△
D
EX
lies on the perpendicular bisector of
O
A
OA
O
A
.
geometry
BxMO