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Polish MO Finals
1981 Polish MO Finals
1
1
Part of
1981 Polish MO Finals
Problems
(1)
circle with every point on intersection of 2 planes
Source: Polish MO Finals 1981 p1
8/24/2024
Two intersecting lines
a
a
a
and
b
b
b
are given in a plane. Consider all pairs of orthogonal planes
α
\alpha
α
,
β
\beta
β
such that
a
⊂
α
a \subset \alpha
a
⊂
α
and
b
⊂
β
b\subset \beta
b
⊂
β
. Prove that there is a circle such that every its point lies on the line
α
∩
β
\alpha \cap \beta
α
∩
β
for some
α
\alpha
α
and
β
\beta
β
.
geometry
3D geometry