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In triangle ABC, the circumcenter and orthocenter are collinear with vertex A. Which of the following statements must be true?

(1)  must be an isosceles triangle.
(2)  must be an equilateral triangle.
(3)  must be a right triangle.
(4)  must be an isosceles right triangle.

 

If none of them are true, say none. 

 

I appreciate the help! Also, happy holidays!

 Dec 28, 2018
edited by Guest  Dec 28, 2018
edited by noobieatmath  Dec 28, 2018
edited by noobieatmath  Dec 28, 2018
 #1
avatar+101870 
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"with vertex"....????

 

Which vertex ???

 

 

cool cool cool

 Dec 28, 2018
 #2
avatar+143 
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Oh, my bad. I didn't even write the question properly... just edited though, so it should be good now! 

noobieatmath  Dec 28, 2018
 #3
avatar+101870 
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I think that (2) is the true statement.......

 

The circumcenter is where the perpedicular bisectors meet

 

The orthocenter is where the altiudes intersect

 

In an equilateral triangle, these are the same from any vertex

 

 

 

cool cool cool

 Dec 28, 2018
 #4
avatar+143 
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That's what I had originally said, but it said that I was wrong... confusing...

noobieatmath  Dec 28, 2018

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