**Q) In the given figure PA, QB and RC are each perpendicular to AC. If AP = x, BQ = y and CR = z, then prove that 1/x + 1/z = 1/y**

**Ans: **

**Step 1:** In Δ APC and Δ BQC,

∠ PCA = ∠ QCB (common angle)

∠ PAC = ∠ QBC (90^{0})

By AA identity, Δ APC ~ Δ BQC

Hence,

………….. (i)

**Step 2:** In Δ RCA and Δ QBA,

∠ RAC = ∠ QAB (common angle)

∠ RCA = ∠ QBA (90^{0})

By AA identity, Δ RCA ~ Δ QBA

Hence,

………….. (ii)

By adding equations (i) and (ii), we get:

Dividing by x y z on both sides, we get:

**Hence Proved !**

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