Question related to nine point centre

[prashant singh]

1. Prove that nine point centre is the mid point of orthocentre and circumcentre.

Homework Equations

3. I know about euler line and its proof that centeroid,circumcentre and orthocentre are collinear and centeroid divides orthocentre and circumcentre in the ratio 2:1

 

[Mark44]

In case anyone else wasn't familiar with the term nine-point center, here's a wiki article: https://en.wikipedia.org/wiki/Nine-point_center

@prashant singh, have you looked at this article?

 

[prashant singh]

Yes I read the whole article but there was no proof.

In case anyone else wasn't familiar with the term nine-point center, here's a wiki article: https://en.wikipedia.org/wiki/Nine-point_center

@prashant singh, have you looked at this article?

 

[haruspex]

I know the requirement is awkward for proofs, but on these homework forums you are supposed to show some attempt. Do you have any thoughts at all on the matter?
You could also try following some of the referenced links from the Wikipedia article.

 

[prashant singh]

I know the requirement is awkward for proofs, but on these homework forums you are supposed to show some attempt. Do you have any thoughts at all on the matter?
You could also try following some of the referenced links from the Wikipedia article.

I know the requirement is awkward for proofs, but on these homework forums you are supposed to show some attempt. Do you have any thoughts at all on the matter?
You could also try following some of the referenced links from the Wikipedia article.

I don't have any attempts , I don't know how to start but I know euler line and I have tried to link them but I didn't get the answer. Do you have hints.

 

[Mark44]

Yes I read the whole article but there was no proof.

I didn't post the article because I thought it had a proof. I posted it because I thought it might help you do your proof. Part of that article gives the coordinates of the nine-point center. If you can get the coordinates of the other points you're concerned with, you're pretty much done.

Please show us what you have tried.

 

[prashant singh]

If you know the proof then tell me directly or give me a good hint. How they got those trilenear coordinates. I am not getting it

 

[Mark44]

If you know the proof then tell me directly

That's not how it works here. From the rules (https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/):

Giving Full Answers:
On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given.

You have been given some hints -- it's up to you to show some effort. So far, I haven't seen any effort on your part.

 

[prashant singh]

This is a prove related question , how can I made a attempt. I have tried to relate it with orthocenter and circumcentre but I didn't get the answer. I have used the fact that centeroid divides orthocentre and circumcentre in the ratio 2:1

 

[Mark44]

Since you still haven't shown any work after repeated requests to do so, I am closing this thread.