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Canada National Olympiad
2024 Canada National Olympiad
1
1
Part of
2024 Canada National Olympiad
Problems
(1)
Reflecting triangle sides across angle bisector
Source: Canada MO 2024/1
3/8/2024
Let
A
B
C
ABC
A
BC
be a triangle with incenter
I
I
I
. Suppose the reflection of
A
B
AB
A
B
across
C
I
CI
C
I
and the reflection of
A
C
AC
A
C
across
B
I
BI
B
I
intersect at a point
X
X
X
. Prove that
X
I
XI
X
I
is perpendicular to
B
C
BC
BC
.
geometry
incenter
geometric transformation
reflection
angle bisector