CBSE Class 10 Maths (Standard) 2024 · Paper 30/1/1 · Question 34(b)

Triangles 5 marks Medium

In the given figure

P A

QB

and

R C

are each perpendicular to

A C

. If

A P = x

B Q = y

and

C R = z

, then prove that

\frac{1}{x} + \frac{1}{z} = \frac{1}{y}

Three perpendiculars PA, QB, RC to line AC

Answer

From the two similarities,

\frac{y}{x} + \frac{y}{z} = \frac{A B + B C}{A C} = 1

, so

\frac{1}{x} + \frac{1}{z} = \frac{1}{y}

. Hence proved.

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