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Poland Contests
Polish MO Finals
1995 Polish MO Finals
3
3 rays in space
3 rays in space
Source: Poland MO 1995
August 24, 2005
geometry unsolved
geometry
Problem Statement
P
A
,
P
B
,
P
C
PA, PB, PC
P
A
,
PB
,
PC
are three rays in space. Show that there is just one pair of points
B
′
,
C
B', C
B
′
,
C
' with
B
′
B'
B
′
on the ray
P
B
PB
PB
and
C
′
C'
C
′
on the ray
P
C
PC
PC
such that
P
C
′
+
B
′
C
′
=
P
A
+
A
B
′
PC' + B'C' = PA + AB'
P
C
′
+
B
′
C
′
=
P
A
+
A
B
′
and
P
B
′
+
B
′
C
′
=
P
A
+
A
C
′
PB' + B'C' = PA + AC'
P
B
′
+
B
′
C
′
=
P
A
+
A
C
′
.
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