`A(3, 4),B(0,0) and c(3,0)` are vertices of `DeltaABC.` If 'P' is the point inside the `DeltaABC`, such that `d(P, BC)le` min. `{d(P, AB), d (P, AC)}`. Then the maximum of `d (P, BC)` is.(where `d(P, BC)` represent distance between `P and BC)`.

Options

A. 1
B. `1//2`
C. 2
D. none of these

Explanation

To solve the problem, we need to find the maximum distance \( d(P, BC) \) where \( P \) is a point inside triangle \( ABC \) such that \( d(P, BC) \leq \min\{d(P, AB), d(P, AC)\} \).

### Step-by-Step Solution:

1. **Identify the vertices of the triangle:**
- The vertices are given as \( A(3, 4) \), \( B(0, 0) \), and \( C(3, 0) \).

2. **Determine the equations of the sides of the triangle:**
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