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Kvant 2020
M2611
M2611
Part of
Kvant 2020
Problems
(1)
Easy Geometry , concyclicity wanted
Source: 2020 Caucasus Mathematical Olympiad Seniors Problem 7
3/16/2020
In
△
A
B
C
\triangle ABC
△
A
BC
with
A
B
≠
A
C
AB\neq{AC}
A
B
=
A
C
let
M
M
M
be the midpoint of
A
B
AB
A
B
, let
K
K
K
be the midpoint of the arc
B
A
C
BAC
B
A
C
in the circumcircle of
△
A
B
C
\triangle ABC
△
A
BC
, and let the perpendicular bisector of
A
C
AC
A
C
meet the bisector of
∠
B
A
C
\angle BAC
∠
B
A
C
at
P
P
P
. Prove that
A
,
M
,
K
,
P
A, M, K, P
A
,
M
,
K
,
P
are concyclic.
geometry