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Mathematical Excellence Olympiad
2020 IMEO
Problem 1
Problem 1
Part of
2020 IMEO
Problems
(1)
Easy but cute geometry
Source: IMEO 2020 Problem 1
7/15/2020
Let
A
B
C
ABC
A
BC
be a triangle and
A
′
A'
A
′
be the reflection of
A
A
A
about
B
C
BC
BC
. Let
P
P
P
and
Q
Q
Q
be points on
A
B
AB
A
B
and
A
C
AC
A
C
, respectively, such that
P
A
′
=
P
C
PA'=PC
P
A
′
=
PC
and
Q
A
′
=
Q
B
QA'=QB
Q
A
′
=
QB
. Prove that the perpendicular from
A
′
A'
A
′
to
P
Q
PQ
PQ
passes through the circumcenter of
△
A
B
C
\triangle ABC
△
A
BC
.Fedir Yudin
IMEO
geometry