In a `triangleABC` the angles at B and C are acute. If BE and CF be drawn perpendiculars on AC and AB respectivel, prove that
`BC^(2) = Abxx BF + AC xx EC`

Explanation

To prove that in triangle \( ABC \), where \( BE \) and \( CF \) are perpendiculars from points \( B \) and \( C \) to sides \( AC \) and \( AB \) respectively, the equation \( BC^2 = AB \cdot BF + AC \cdot EC \) holds, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Right Triangles**:
- We have two right triangles: \( \triangle BFC \) and \( \triangle BEC \).
- In \( \triangle BFC \), \( BF \) is perpendicular to \( AC \).
- In \( \triangle BEC \), \( BE \) is perpendicular to \( AB \).
...