### Orthocenter

The orthocenter is the point of intersection of the three heights of a triangle. A height is each of the perpendicular lines drawn from one vertex to the opposite side (or its extension).

### Centroid The centroid is the point of intersection of the three medians.

A median is each of the straight lines that joins the midpoint of a side with the opposite vertex

The centroid divides each median into two segments, the segment joining the centroid to the vertex is twice the length of the length of the line segment joining the midpoint to the opposite side.

the segment connecting the centroid to the apex is twice the length of the line segment joining the midpoint to the opposite side.

BG = 2GA

### Circumcenter The circumcenter is the point of intersection of the three perpendicular bisectors.

A perpendicular bisectors of a triangle is each line drawn perpendicularly from its midpoint.

The circumcenter is the center of a triangle's circumcircle (circumscribed circle).

### Incenter The incenter is the point of intersection of the three angle bisectors.

The angle bisectors of a triangle are each one of the lines that divide an angle into two equal angles.

The incenter is the center of the circle inscribed in the triangle.

### Line of Euler The orthocenter, the centroid and the circumcenter of a non-equilateral triangle are aligned; that is to say, they belong to the same straight line, called line of Euler.

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.