Math, asked by diyadhawan1, 1 year ago

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

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Answered by KunalTheGreat
5

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

∴ AA1 \\  BB1 \\ CC1 .

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

Proof :
AA1 \\  BB1

∴ ΔCBB~ Δ CAA1    ( AA similarity).

∴ CB/ AC = BB/ AA1   = z / x ---------------(1)

Also  BB1 \\ CC1 .

∴ ΔABB~ Δ ACC1 .  ( AA similarity).

∴ AB/ AC = BB/ CC1   = z / y ---------------(2)

Adding (1) and (2) we get

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

dividing (3) by z we get 
   
1 / x + 1 / y = 1 / z.
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Answered by ronnie67
8

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