P and Q are point

There are two triangles here, ∆APQ and ∆ABC. We shall prove these triangles to be similar.

&

⇒

Also, ∠A = ∠A [common angle]

So by AA-similarity criteria,

∆APQ ∼ ∆ABC

Thus,

And we know

⇒ BC = 3×PQ

Hence, proved.