MathDB
Problems
Contests
Undergraduate contests
IMC
1996 IMC
10
10
Part of
1996 IMC
Problems
(1)
IMC 1996 Problem 10
Source: IMC 1996
3/4/2021
Let
B
B
B
be a bounded closed convex symmetric (with respect to the origin) set in
R
2
\mathbb{R}^{2}
R
2
with boundary
Γ
\Gamma
Γ
. Let
B
B
B
have the property that the ellipse of maximal area contained in
B
B
B
is the disc
D
D
D
of radius
1
1
1
centered at the origin with boundary
C
C
C
. Prove that
A
∩
Γ
≠
∅
A \cap \Gamma \ne \emptyset
A
∩
Γ
=
∅
for any arc
A
A
A
of
C
C
C
of length
l
(
A
)
≥
π
2
l(A)\geq \frac{\pi}{2}
l
(
A
)
≥
2
π
.
conics
ellipse
geometry