Can you solve this geometric question on triangles?

Question

In a triangle $ABC$, $D$ is a point on the side $BC$.Given:
$AD=10$,$BD=DC=8$ and $BC*AD=6$.What is the length of $BC$?

a.$5$
b.$10$
c.$15$
d.$20$

That was asked in a newspaper quiz.

Answer 1

No, I cannot solve this.

From the second part $BD=DC=8$ and the fact that $D$ lies on $BC$, we have$BC= BD+DC=16$.
From the first and last part $BC= \frac{6}{AD} = \frac{6}{10}$.

Since neither $16$ nor $\frac{6}{10}$ is equal to $5$, $10$, $15$, $20$ or each other, there is no answer.