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Poland Contests
Polish MO Finals
1954 Polish MO Finals
3
3
Part of
1954 Polish MO Finals
Problems
(1)
3 weights on a uniform circular disc
Source: Polish MO Finals 1954 p3
8/29/2024
A uniform circular disc is suspended in a horizontal position on a string attached to its center
O
O
O
. At three different points
A
A
A
,
B
B
B
,
C
C
C
on the edge of the disc, weights
p
1
p_1
p
1
,
p
2
p_2
p
2
,
p
3
p_3
p
3
are placed, after which the disc remains in equilibrium. Calculate angles
A
O
B
AOB
A
OB
,
B
O
C
BOC
BOC
, and
C
O
A
COA
CO
A
.
geometry