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**Hint:**Let us assume that the distance of a crawling thief from wall is x in the west direction. So, we gathered two triangles. Now, by using the similarity of triangles, find the value of x.

**Complete step by step answer:**

We have:

Height of wall: DE = a

Height of policeman: BC = b

Distance of policeman from wall: BC = c

Now, we have two triangles as: $\Delta ABC$ and $\Delta ADE$

In $\Delta ABC$ and $\Delta ADE$

Since, $DE\parallel BC$

Therefore, $\angle ADE=\angle ABC$ and $\angle AED=\angle ACB$ (alternate interior angles)

So, $\Delta ABC\approx \Delta ADE$ ( by AAA similarity)

Therefore, we can say that:

$\dfrac{AD}{AB}=\dfrac{DE}{BC}=\dfrac{AE}{AC}$

So, we have:

$\begin{align}

& \Rightarrow \dfrac{AD}{AB}=\dfrac{DE}{BC} \\

& \Rightarrow \dfrac{AD}{AD+DB}=\dfrac{DE}{BC} \\

& \Rightarrow \dfrac{x}{x+c}=\dfrac{a}{b} \\

\end{align}$

So, by solving the above equation, we get:

$\begin{align}

& \Rightarrow bx=a\left( x+c \right) \\

& \Rightarrow bx-ax=ac \\

& \Rightarrow x\left( b-a \right)=ac \\

& \Rightarrow x=\dfrac{ac}{b-a} \\

\end{align}$

**So, the correct answer is “Option D”.**

**Note:**

Two triangles are said to be similar if

a) Their corresponding angles are equal, and

b) Their corresponding sides are proportional.

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