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2021-IMOC
G4
G4
Part of
2021-IMOC
Problems
(1)
Prove that XY passes through a fixed point
Source: IMOC 2021 G4
8/11/2021
Let
D
D
D
be a point on the side
A
C
AC
A
C
of a triangle
A
B
C
ABC
A
BC
. Suppose that the incircle of triangle
B
C
D
BCD
BC
D
intersects
B
D
BD
B
D
and
C
D
CD
C
D
at
X
X
X
,
Y
Y
Y
, respectively. Show that
X
Y
XY
X
Y
passes through a fixed point when
D
D
D
is moving on the side
A
C
AC
A
C
.
geometry
incenter
Fixed point