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National and Regional Contests
France Contests
French Mathematical Olympiad
1995 French Mathematical Olympiad
Problem 3
Problem 3
Part of
1995 French Mathematical Olympiad
Problems
(1)
three circles, minimal set of points
Source: French MO 1995 P3
4/22/2021
Consider three circles in the plane
Γ
1
,
Γ
2
,
Γ
3
\Gamma_1,\Gamma_2,\Gamma_3
Γ
1
,
Γ
2
,
Γ
3
of radii
R
R
R
passing through a point
O
O
O
, and denote by
D
\mathfrak D
D
the set of points of the plane which belong to at least two of these circles. Find the position of
Γ
1
,
Γ
2
,
Γ
3
\Gamma_1,\Gamma_2,\Gamma_3
Γ
1
,
Γ
2
,
Γ
3
for which the area of
D
\mathfrak D
D
is the minimum possible. Justify your answer.
geometry