Question

In the given figure, QR is parallel to AB and DR is parallel to AB and DR is parallel to QB.

Prove that: PQ² = PD × PA.

Answer 1

Given, QR is parallel to AB.

Using Basic proportionality theorem,

`=> (PQ)/(PA) = (PR)/(PB)`    ...(1)

Also, DR is parallel to QB.

Using Basic proportionality theorem,

`=> (PD)/(PQ) = (PR)/(PB)`    ...(2)

From (1) and (2), we get,

`(PQ)/(PA) = (PD)/(PQ)`

PQ² = PD × PA