Rectangle inscribed in Triangle

AI Thread Summary
The discussion revolves around finding the locus of intersection points of the diagonals of a rectangle inscribed in triangle ABC. Participants express uncertainty about the problem's complexity, with one individual admitting to struggling with the geometric interpretation. There is a suggestion to share progress to facilitate assistance, indicating a collaborative approach to problem-solving. Initial thoughts on the locus being a line are questioned, leading to doubts about the interpretation. Overall, the conversation highlights the challenge of applying geometric concepts and the desire for clarity in understanding the problem.
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Let PQRS be a rectangle inscribed in a triangle ABC(i.e P is in AC, Q in BC and R,S are in AB). Find the locus of points that are intersection of diagonals of the rectangle. (i.e find the locus of intersection of RQ and PS)
 
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Sounds like a homework problem!

If you would care to post where you've gotten on the problem (even if your thoughts are seemingly trivial), then maybe we could help you work through the point where you're stuck.
 
Hi. Well, it's not a homework problem, that's for sure. I haven't done much progress on this problem, seems quite hard. Or perhaps just my elementary geometry skills suck ? I've tried to somehow interpret this geometric problem in complex numbers' language, you know, but didn't really work as I thought. First I thought the locus should be a line, but now I doubt it. I think it's not. I may be wrong. Thank you !
 

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