Let
C
C
be an arbitrary planar convex body. We prove that
C
C
contains an axially symmetric convex body of area at least
2
3
|
C
|
\frac {2}{3}|C|
. Also approximation by some specific axially symmetric bodies is considered. In particular, we can inscribe a rhombus of area at least
1
2
|
C
|
\frac {1}{2}|C|
in
C
C
, and we can circumscribe a homothetic rhombus of area at most
2
|
C
|
2|C|
about
C
C
. The homothety ratio is at most
2
2
. Those factors
1
2
\frac {1}{2}
and
2
2
, as well as the ratio
2
2
, cannot be improved.