In any triangles, the altitudes, medians, and internal bisectors of the vertices or perpendicular bisectors of the sides are concurrent.

Let us see the special names for these points of concurrence.

**Orthocenter:** It is the point of concurrence of the altitudes of a triangle.

The following diagram shows the position of orthocenter for the respective triangle.

1. For an acute angled triangle the orthocenter lies inside the triangle.

2. For an obtuse angled triangle the orthocenter lies outside the triangle

3. For a right angled triangle orthocenter lies at the hypotenuse of the triangle.**Centroid:** It is the point of concurrence of the medians of a triangle.

Whether the triangle is acute, obtuse of right angled triangle, the centroid always lies inside the triangle.

**Incenter: **It is the point of concurrence of the internal bisectors of the angles of a triangle.

The circle with center as I and radius equal to the perpendicular distances of I from the sides, touches the sides of the triangle. Hence the point is called

**Incenter **of the triangle.

For all types of triangles, acute, obtuse or right triangle, the Incenter always lies inside the circle.

### Circumcenter: It is the point of concurrence of the perpendicular bisectors of the sides of a triangle.

SA = SB = SC

We can see that the circle with center at S (circumcenter) is equidistant from the vertices and hence the circle passes through the vertices of the triangle. The circle so drawn is called as circumcircle.

1. For an acute angled triangle, the circumcenter lies in the interior of the triangle.

2. For a right angled triangle the circumcenter is the midpoint of the hypotenuse.

3. For an obtuse angled triangle, the circumcenter will lie outside the triangle.### Equilateral triangle: For an equilateral triangle, the above four points coincide. That is the points G, O, I and S are the same.