Let `A B C` be a given isosceles triangle with `A B=A C` . Sides `A Ba n dA C` are extended up to `Ea n dF ,` respectively, such that `B ExC F=A B^2dot` Prove that the line `E F` always passes through a fixed point.

Explanation

To solve the problem, we need to prove that the line EF always passes through a fixed point when the sides AB and AC of the isosceles triangle ABC are extended to points E and F, respectively, such that \( BE \cdot CF = AB^2 \).

### Step-by-Step Solution:

1. **Define the Triangle and Points**:
Let \( A(0, b) \), \( B(-a, 0) \), and \( C(a, 0) \) be the vertices of the isosceles triangle ABC, where \( AB = AC \).

2. **Extend the Sides**:
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