Geometry question

Question

In the given figure , AP, BQ and CR are perpendicular to line AC. And AP=$x$ , BQ=$y$, CR=$z$ then find the value of $\frac{1}{x} + \frac{1}{z}$ in terms of $y$. I have no idea how to solve it. But the limitation is this is to do with the use of similarity concepts. Don't use trigonometry.

Answer 1

y/z = AB / (AB+BC)

y/x = BC / (AB+BC)

y/z + y/x = AB/(AB+BC) + BC/(AB+BC) = 1

1/z + 1/x = 1/y

Answer 2

Using the Side-Splitter Theorem can write $y/z = AB/AC$ and $y/x = BC/AC$. From there the answer is $1/x + 1/z = 1/y$.