Solution:-

From the question it is given that,

∠1 = ∠2 and ∠3 = ∠4

We have to prove that, PT x QR = PR x ST

Given, ∠1 = ∠2

Adding ∠6 to both LHS and RHS we get,

∠1 + ∠6 = ∠2 + ∠6

∠SPT = ∠QPR

Consider the ∆PQR and ∆PST,

From above ∠SPT = ∠QPR

∠3 = ∠4

Therefore, ∆PQR ~ ∆PST

So, PT/PR = ST/QR

By cross multiplication we get,

PT x QR = PR x ST

Hence, it is proved that PT x QR = PR x ST