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Thailand Online MO
2023 Thailand Online MO
6
6
Part of
2023 Thailand Online MO
Problems
(1)
circumcenter of AXY lies on circumcircle of ABC
Source: 2023 Thailand Online MO P6
2/12/2023
Let
A
B
C
ABC
A
BC
be a triangle. Construct point
X
X
X
such that
B
X
=
B
A
BX=BA
BX
=
B
A
and
X
X
X
and
C
C
C
lies on the same side of line
A
B
AB
A
B
. Construct point
Y
Y
Y
such that
C
Y
=
C
A
CY=CA
C
Y
=
C
A
and
Y
Y
Y
and
B
B
B
lies on different sides of line
A
C
AC
A
C
. Suppose that triangle
B
A
X
BAX
B
A
X
and triangle
C
A
Y
CAY
C
A
Y
are similar, prove that the circumcenter of triangle
A
X
Y
AXY
A
X
Y
lies on the circumcircle of triangle
A
B
C
ABC
A
BC
.
geometry