MathDB

Let

B

be a bounded closed convex symmetric (with respect to the origin) set in

\mathbb{R}^{2}

with boundary

\Gamma

. Let

B

have the property that the ellipse of maximal area contained in

B

is the disc

D

of radius

1

centered at the origin with boundary

C

. Prove that

A \cap \Gamma \ne \emptyset

for any arc

A

C

of length

l(A)\geq \frac{\pi}{2}

Problem Statement