Triangle Y
Here is triangle Y.
What is special about triangle Y in comparison to the previous two triangles, W and X.
Oooooo! You know this one!
Here is the construction of triangle Y's orthocenter.
Here is the construction of triangle Y's circumcenter.
Here is the construction of triangle Y's centroid.
Here is all three of those constructions together for triangle Y.
Hmmmm INTERESTING...
What is the first thing you notice about triangle Y and its three triangle centers?
Move triangle Y's vertices around. Does anything change?
Based on your observations of triangle Y and these constructions... make a conjecture!
What generalized statement might you be able to assume?