Two of the most important examples in $II_1$ factors are the amenable $II_1$ factor and the free group factors. The first one is well-understood, thanks to Connes' fundamental work, while the structure of free group factors is still under intense study. Regarding amenable subalgebras inside free group factors, Jesse Peterson conjectured that any diffuse amenable subalgebra of a free group factor has a unique maximal amenable extension. In this talk I will show that any diffuse subalgebra of the radial masa in a free group factor with finitely many generators, has a unique maximal amenable extension.