In the figure $P A, Q B$ and $R C$ are each perpendicular to $A C$ . Then $\frac{1}{x} + \frac{1}{z} =$

1

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y

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\frac{1}{y}

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x + z

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Solution

The correct option is C $\frac{1}{y}$
$S i n c e P A, Q B a n d R C a r e e a c h p e r p e n d i c u l a r t o A C . H e n c e P A ∥ Q B ∥ R C I n △ A P C \frac{y}{x} = \frac{B C}{A C} (B y b a s i c P r o p o r t i o n a l i t y T h e o r m) . . . (1) I n △ A R C \frac{y}{z} = \frac{A B}{A C} (B P T T h e o r m) . . . . (2) A d d i n g (1) a n d (2) \frac{y}{x} + \frac{y}{z} = \frac{A B + B C}{A C} y [\frac{1}{x} + \frac{1}{z}] = \frac{A C}{A C} = 1 \Rightarrow \frac{1}{x} + \frac{1}{z} = \frac{1}{y} H e n c e o p t i o n (C) i s c o r r e c t a n s w e r$

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