Centers of a Triangle – Meaning/Definition
In the primary and middle classes students get familiar with the center of a circle i.e. the point inside the circle which is equidistant from all other points on the circle is known as a center of a circle or the point of intersection of any two diameters of a circle.
But does there exist any point inside or outside the triangle which can be considered as the center of the circle? Answer to this question is – YES, Infact there exists five types of center of a triangle:
1. Centroid (G)
2. Incenter (I)
3. Circumcenter (O)
4. Orthocenter (H)
5. Ex-centers (E)

Centroid: The point of intersection of medians of a triangle is known as centroid of a triangle.
In the given figure ABC is a triangle, AD, BE and CF are the medians and G is
a point of intersection of medians known as CENTROID.
Centroid is generally represented by a symbol G.

Incenter: The point of intersection of angle bisectors of a triangle is known as an incenter.
Incentre is generally represented by a symbol I.
In the given figure ABC is a triangle, AD, BE and CF are the angle bisectors an
d I is a point of intersection of angle bisectors known as INCENTER.
Circumcenter: The point of intersection of perpendicular
bisectors of sides of a triangle is known as circumcenter.
Circumcenter is generally represented by a symbol O.
In the given figure ABC is a triangle, perpendicular bisectors intersect at O which is known as CIRCUMCENTER.

Orthocenter: The point of intersection of altitudes of a triangle is known
as an orthocenter of a triangle.
Orthocenter is generally represented by a symbol H.
In the given figure ABC is a triangle, AD, BE and CF are the altitudes and H is a point of intersection of altitudes known as ORTHOCENTER.

Ex-center: The
point of intersection an interior angle bisector and the exterior opposite angle bisectors is known as ex-center of a triangle.
Ex-center is generally represented by a symbol E.
In the given figure ABC is a triangle, angle bisector of A and the angle bisector of
exterior angles B and C intersect each other at E1 which is known as EXCENTER.
NOTE: There are three Ex-centers in a given triangle.