In the figure - PA,, QB and RC are perpendiculars to AC. prove that 1/x + 1/z = 1/y

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In the figure - PA,, QB and RC are perpendiculars to AC prove
that 1/x + 1/z = 1/y

Aakash Sharma · Accepted Answer

Since PA, QB, RC âŠ¥ AC â‡’PA II QB II RC Now in Î”PAC QB II PA $\Rightarrow \frac{B C}{A C} = \frac{y}{x} \Rightarrow B C = \frac{y}{x} \times A C (1)$ Also in Î”ARC QB II RC $\Rightarrow \frac{A B}{A C} = \frac{y}{z} \Rightarrow A B = \frac{y}{z} \times A C (2)$ Adding (1) and (2) we get $B C + A B = \frac{y}{x} \times A C + \frac{y}{z} \times A C \Rightarrow A C = y \times A C (\frac{1}{x} + \frac{1}{z}) \Rightarrow \frac{1}{x} + \frac{1}{z} = \frac{1}{y}$