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.

score 2 · Accepted Answer · answered Sep 22 '13 at 05:07

2

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

answered Sep 22 '13 at 05:07

gene

36

Hoda · Answer 2 · 2013-09-22T05:10:10.477

0

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

edited Sep 22 '13 at 05:10

answered Sep 22 '13 at 04:59

Hoda

1,098

Geometry question

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