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USAMO
2012
Problem - 3431
Let
P
be a point in the plane of
△
A
B
C
, and
γ
a line passing through
P
. Let
A
′
,
B
′
,
C
′
be the points where the reflections of lines
P
A
,
P
B
,
P
C
with respect to
γ
intersect lines
B
C
,
A
C
,
A
B
respectively. Prove that
A
′
,
B
′
,
C
′
are collinear.
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