I am solving this question:
Let $ABC$ be an acute angled triangle and $CD$ be the altitude through $C$. If $AB=8$ and $CD=6$, find the distance between the midpoints of BC and AD.
So I observed that there are an infinite number of such triangles which satisfy $AB=8$ and $CD=6$ with $CD \perp AB$. So I can move $B$ closer to $D$ and $A$ away from $D$ to keep $AB$ constant. So what I did is I coincided $B$ and $D$ so the problem became much easier to solve. And I got the correct answer of $5$.
But if I coincide $B$ and $D$ then $\triangle ABC$ is no longer acute angled but rather right angled. So how can I use this approach of solving the problem in a subjective test without breaking the assumption that $ABC$ is acute angled?
I think that this is quite clear: