MHB Find the Max of $PC$ in $\triangle ABC$

[Albert1]

$\triangle ABC$ with $AB=BC=CA$
if another point $P$ and $PA=2, \,\, PB=3$
please find :$max(PC)$

 

[Albert1]

$\triangle ABC$ with $AB=BC=CA$ if another point $P$ and $PA=2, \,\, PB=3$ please find :$max(PC)$

my solution: