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Poland Contests
Polish MO Finals
1959 Polish MO Finals
2
2
Part of
1959 Polish MO Finals
Problems
(1)
AP + BM+CN= fixed, equilateral related
Source: Polish MO Finals 1959 p2
8/29/2024
In an equilateral triangle
A
B
C
ABC
A
BC
, point
O
O
O
is chosen and perpendiculars
O
M
OM
OM
,
O
N
ON
ON
,
O
P
OP
OP
are dropped to the sides
B
C
BC
BC
,
C
A
CA
C
A
,
A
B
AB
A
B
, respectively. Prove that the sum of the segments
A
P
AP
A
P
,
B
M
BM
BM
,
C
N
CN
CN
does not depend on the position of point
O
O
O
.
geometry
fixed
Equilateral