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

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Albert1
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$\triangle ABC$ with $AB=BC=CA$
if another point $P$ and $PA=2, \,\, PB=3$
please find :$max(PC)$
 
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Albert said:
$\triangle ABC$ with $AB=BC=CA$ if another point $P$ and $PA=2, \,\, PB=3$ please find :$max(PC)$

my solution:
 

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