Question about a proof of the converse of Thales' theorem

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    Euclidean geometry
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The discussion centers on a specific part of Eddie Woo's proof of Thales' theorem and its converse, particularly the expression (x–u)(x–v) = 0. The user seeks clarification on the reasoning behind considering this expression at that point in the proof. It is implied that understanding this step is crucial for grasping the overall proof. The conversation highlights the importance of each mathematical step in the context of the theorem's proof. Clarifying this aspect can enhance comprehension of Thales' theorem and its converse.
murshid_islam
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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?

 

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