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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!

noobieatmath Dec 28, 2018

#1

#2**0 **

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**+1 **

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

CPhill Dec 28, 2018

#4**0 **

That's what I had originally said, but it said that I was wrong... confusing...

noobieatmath
Dec 28, 2018