The chord $[CD]$ is parallel to the diameter $[AB]$ of a circle with center $O$. The tangent line at $A$ meet $BC$ and $BD$ at $E$ and $F$. If $|AB|=10$, calculate $|AE|\cdot |AF|$.
1. **Identify the given information and the goal:**
   - The chord $[CD]$ is parallel to the diameter $[AB]$ of a circle with center $O$.
   - The tangent line at $A$ meets $BC$ and $BD$ at $E$ and $F$ respectively.
   - $|AB| = 10$.
   - We need to calculate $|AE| \cdot |AF|$.

2. **Analyze the angles and properties of the circle:**
   - Since $[CD]$ is parallel to $[AB]$, $\angle ACD + \angle CAB = \pi$ and $\angle ACD + \angle ABD = \pi$.
   - Therefore, $\angle CAB = \angle ABD$.
   - This implies that $ABDC$ is an isosceles trapezoid with $AB \parallel CD$ and $AD = BC$.

3. **Use the properties of tangents and perpendiculars:**
   - The tangent at $A$ is perpendicular to the radius $OA$.
   - Since $AD \perp BF$ and $AC \perp BE$, we have $\angle FBA = \angle ABD$ and $\angle BAC = \angle AEC = \angle BEA$.

4. **Establish the similarity of triangles:**
   - From the above angle relationships, $\triangle EAB \sim \triangle BAF$ by AA similarity criterion (Angle-Angle similarity).
   - This similarity implies that the corresponding sides are proportional.

5. **Calculate the product of segments:**
   - From the similarity $\triangle EAB \sim \triangle BAF$, we have:
     \[
     \frac{AE}{AB} = \frac{AB}{AF}
     \]
   - Cross-multiplying gives:
     \[
     AE \cdot AF = AB^2
     \]
   - Given $|AB| = 10$, we substitute:
     \[
     AE \cdot AF = 10^2 = 100
     \]

Conclusion:
\[
\boxed{100}
\]