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## Geometry (all content)

### Course: Geometry (all content)>Unit 4

Lesson 8: Bringing it all together

# Euler's line proof

Proving the somewhat mystical result that the circumcenter, centroid, and orthocenter all sit on the same line. Created by Sal Khan.

## Want to join the conversation?

• Is there any easy way of remembering which center is called what?
I keep forgetting...
• No offense, but this is the scariest mnemonic device I've ever seen.
• Isn't the centroid of ABC also the centroid of DEF?
• It sure looks like it.
• So what about the incenter? Surely it must also have some fascinating properties?
• The incenter is the same distance from all the sides of the triange.
• Where can I use the Euler line in the world? And why is it important
• It is important to learn because a triangle is the basic shape in geometry, but it is filled with so many fascinating properties. It might not assist you in the world, but it is interesting to know.
• what is the 9 point circle? and does the incenter not lie on euler's line?
• In geometry, the nine-point circle is a circle that can be constructed for any given triangle. It is named this because it passes through nine points defined from the triangle. These nine points are:
The midpoint of each side of the triangle
The foot of each altitude
The midpoint of the line segment from each vertex of the triangle to the orthocenter (where the three altitudes meet; these line segments lie on their respective altitudes).

I hope this helps:)
• At , Maybe you used that if vertical angles are same or alternate interior angles are same, vertices are on the same line. I can understand intuitively but can not understand logically..... Please explain more in detail.
• getting a little confused about how he can correlate the 2 distances... He can relate them with a ratio because the smaller medial triangle´s orthocenter is concurrent to the larger triangle´ circumcenter, right? So the perpendicular bisector of the larger triangle is also the height of the smaller medial triangle?