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Requirements

A triangle need be scalene or obtuse

This property is already shown and proven in right angled triangle

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    $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$ Commented Nov 2 at 18:46
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    $\begingroup$ According to Wikipedia, "The Encyclopedia of Triangle Centers (ETC) is an online list of thousands of points or "centers" associated with the geometry of a triangle. ... As of 19 May 2025, the list identifies $68,547$ triangle centers and is managed cooperatively by an international team of geometry researchers." So, which four of those $68547$ centers are you asking about? Also, what is the "value" of a center? Please edit the body of your question to clarify these issues. $\endgroup$ Commented Nov 3 at 2:02

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