Question

prove that 1/x+1/z =1/y

Answer 1

Given that AA1,BB1,CC1 are each perpendicular to AC.

∴ AA1 \\  BB1 \\ CC1 .

To Prove : 1 / x + 1 / y = 1 / z.

Proof :
AA1 \\  BB1

∴ ΔCBB1 ~ Δ CAA1    ( AA similarity).

∴ CB1 / AC = BB1 / AA1   = z / x ---------------(1)

Also  BB1 \\ CC1 .

∴ ΔABB1 ~ Δ ACC1 .  ( AA similarity).

∴ AB1 / AC = BB1 / CC1   = z / y ---------------(2)

Adding (1) and (2) we get

z / x + z / y = CB1 / AC + AB1 / AC = ( CB1 + AB1 ) / AC  = AC / AC = 1  --------(3)

dividing (3) by z we get 
   
1 / x + 1 / y = 1 / z.
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Answer 2

Answer:

Step-by-step explanation:

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