CBSE Class 10 Maths (Standard) 2025 · Paper 30/3/1 · Question 34(a)

Triangles 5 marks Medium

In the given figure,

P A

QB

and

R C

are perpendicular to

A C

. If

P A = x

units,

QB = y

units and

R C = z

units, prove that

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

PA, QB, RC perpendicular to AC; Q on PC and AR.

Answer

Using

△ A B Q \sim △ A C R

and

△ C B Q \sim △ C A P

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

, so

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

. Hence proved.

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