\( A(3,4), B(0,0) \) and \( C(3,0) \) are vertices of \( \triangle ...

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\( A(3,4), B(0,0) \) and \( C(3,0) \) are vertices of \( \triangle A B C \). If ' \( P \) ' is the point inside the \( \triangle A B C \), such that \( d(P, B C) \leq \min .\{d(P, A B), d(P, A C)\} \). Then the maximum of \( d(P, B C) \) is.
\( \mathrm{P} \) (where \( \mathrm{d}(\mathrm{P}, \mathrm{BC} \) ) represent distance between \( \mathrm{P} \) and \( \mathrm{BC} \) ).

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