MHB What is the relationship between the incenter and orthocenter of a triangle?

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SUMMARY

The discussion centers on the geometric relationship between the incenter and orthocenter of a triangle, specifically addressing the angle between the extended line CH and line HI. The user seeks to demonstrate that this angle measures $\frac{\angle B}{2}$. It is established that while it is impossible to trisect an angle using only a non-graduate ruler and compass, certain angles can be trisected, which is deemed unrelated to the current geometric proof being sought.

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Albert1
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What I see before 'attacking' the problem is that, without any serious failure of me, the 'demonstration' [if any...] would also demonstrate that trisection of an angle with only non graduate ruler and compass is possible... or not?... Kind regards $\chi$ $\sigma$
 
chisigma said:
trisection of an angle with only non graduate ruler and compass is possible... or not?...
It is impossible to trisect any angle with only non graduate ruler and compass ,but some angles are possible, and this is unrelated to this problem .
 
Last edited:
Albert said:
30kdffq.jpg
I need to show that the angle between $CH$(extended) and $HI$ measures $\frac{\angle B}{2}$. I am trying to give a purely geometric proof of this. Any hints on these lines?
 

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