Question

In the given figure, each one of PA, QB and RC is perpendicular to AC. If AP = x, QB = z, RC = y, AB = a and BC = b, show that 1/x + 1/y= 1/z.

Answer 1

In ∆ PAC and ∆QBC, we have: 

∠A = ∠B (Both angle are 90°) 

∠P = ∠Q (corresponding angles) 

And 

∠C = ∠C (common angles) 

Therefore, ∆PAC~ ∆QBC

In ∆ RCA and ∆QBA, we have:

∠C = ∠B (Both angle are 90°) 

∠R = ∠Q (corresponding angles) 

And 

∠A = ∠A (common angles) 

Therefore, ∆RCA ~ ∆QBA

From equation (1) and (2), we have:

Use the value of a/b from equation (3), we have