CBSE Class 10 Maths (Standard) 2019 · Paper 30/2/1 · Question 14(a)

Triangles 3 marks Medium

Two right triangles

A B C

and

D B C

are drawn on the same hypotenuse

B C

and on the same side of

B C

. If

A C

and

B D

intersect at

P

, prove that

A P \times P C = B P \times D P

Answer

Since

△ A P B \sim △ D P C

(AA),

\frac{A P}{D P} = \frac{P B}{P C}

, hence

A P \times P C = B P \times D P

. Proved.

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