Question

in fig PA ,QB,RC are each perpendicular to AC .prove that 1\x+1/z=1/y.
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Answer 1

Step-by-step explanation:

Consider △CAP and △CBQ

∠CAP=∠CBQ=90∘

∠PCA=∠QCB (common angle)

So by AA, △CAP∼△CBQ

Hence APBQ=ACBC

xy=ACBC  (1)

Now consider △ACR and △ABQ

∠ACR=∠ABQ=90∘

∠QAB=∠RAC (common angle)

So by AA, △ACR∼△ABQ

Hence CRBQ=ACAB

zy=ACAB  (2)

Adding (1) and (2)

xy+zy=ACBC+ACAB

y(