Question

prove 1/x + 1/y =1/z ​

Answer 1

Answer:

please check whether it is

1/x+1/y =1/z or

1/x+1/z = 1/y

Step-by-step explanation:

since PA, QB and RC are perpendicular on AC, they are parallel to each other also.

now in triangles PAC and QBC

angle PCA = angle QCB (common)

angle PAC = angle QBC (90°)

angle APC = angle BQC (corresponding angle)

hence the two triangles are similar

so, PA/QB = AC/BC

AC/BC = x/y

or, BC/AC = y/x........(1)

similarly we can prove that triangles RCA and QBA are similar hence,

AC/AB = RC/QB

AC/AB = z/y

or, AB/AC = y/z.......(2)

adding (1) and (2)

BC/AC + AB/AC = y/x + y/z

(BC+AB)/AC = y(1/x+1/z)

AC/AC = y(1/x+1/z). (AB+BC= AC)

1 = y(1/x+1/z)

1/y = 1/x+1/z