Question

50 points...

PA, QB, RC are perpendicular . show
$\frac{1}{x} + \frac{1}{z} = \frac{1}{y}$

Answer 1

Answer:

see steps below

Step-by-step explanation:

In ΔPAC and ΔQBC

∠PCA = ∠QCB

∠PAC = ∠QBC

ΔPAC congurent to ΔQBC

PA/QB = AC/BC

x/y = AB/BC 

y/x = BC/AC

In ΔRCA and ΔQBA

∠RAC = ∠QAB

∠RCA = ∠QBA

ΔRCA is congruent to ΔQBA

RC/QB = AC/AB

z/y= AC/AB

y/z= AB/AC

adding both eq

y/z + y/z = BC + AC/ AC = 1 

y/z + y/z = 1

multiplying both sides by y

1/x + 1/z = 1/y

hope it helps plz mark as brainliest if you liked the solution

Answer 2

Heya Mate !!!

Here's Your Answer ⏬

≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈
Step by Step Explanation ;-
≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈

In ΔPAC and ΔQBC ,

=> ∠PCA = ∠QCB.
=> ∠PAC = ∠QBC.
=> ΔPAC congurent to ΔQBC.
=> PA/QB = AC/BC.

=> x/y = AB/BC.
=> y/x = BC/AC.

In ΔRCA and ΔQBA ,

=> ∠RAC = ∠QAB
=> ∠RCA = ∠QBA
=> ΔRCA is congruent to ΔQBA.
=> RC/QB = AC/AB

=> z/y= AC/AB
=> y/z= AB/AC

Now , adding the equations ;-

=> y/z + y/z = BC + AC/ AC = 1 

=> y/z + y/z = 1

Multiplying RHS and LHS by y.

=> 1/x + 1/z = 1/y

< Hope It Helps >