Question about a proof of the converse of Thales' theorem

[murshid_islam]

Homework Statement

Proof of the converse of Thales' theorem

Relevant Equations

(x–u)(x–v) = 0

I was watching this series of videos of Eddie Woo proving Thales' theorem and its converse. I didn't understand this part (at 2:15) where he considered (x–u)(x–v) = 0. He later used the result he got from considering that. But why consider it in the first place?