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Kvant Problems
Kvant 2023
M2739
M2739
Part of
Kvant 2023
Problems
(1)
AMPK is circumscribed
Source: ARO Regional stage 2023 9.8
2/16/2023
In an acute triangle
A
B
C
ABC
A
BC
, let
M
M
M
and
N
N
N
be the midpoints of
A
B
AB
A
B
and
A
C
AC
A
C
and let
B
H
BH
B
H
be its altitude from
B
B
B
. Its incircle touches
A
C
AC
A
C
at
K
K
K
and the line through
K
K
K
parallel to
M
H
MH
M
H
meets
M
N
MN
MN
at
P
P
P
. Prove that
A
M
P
K
AMPK
A
MP
K
has an incircle.
geometry
Russia