# Centroid, Incentre, Circumcentre and Orthocentre of a Triangle

## Centriod of a Triangle

Centroid of a triangle is a point where the medians of the triangle meet. It's usually denoted by the letter G.
Median is a line segment joining the vertex of a triangle to the mid-point of the opposite side

## fig. 1 centroid of a triangle

In the above fig. 1, ABC is a triangle and D, E and F are the mid-points of the sides BC, AC and AB respectively.
The medians AE, BF and CD always intersect at a single point and that point is called centroid G of the triangle.
The centroid of a triangle is also known as the centre of mass or gravity of the triangle.

## Incentre of a triangle

Incentre of a triangle is a point where the three angle bisectors of the triangle meet.

## fig. 2 incentre of a triangle

In the above ABC (in fig. 2), the angle bisectors of the A, B and C meet at the point I. This point I is the incentre of the triangle.

## Circumcentre of a triangle

The circumcentre of a triangle is the point where the perpendicular bisectors of the sides of the triangle meet.

## fig. 3 circumcentre of a triangle

In the above ABC (in fig. 3), the perpendicular bisectors of the sides AB, BC and CD meet at point H. This point H is called the circumcentre of the triangle.

## Orthocentre of a triangle

The orthocentre of a triangle is a point where the altitudes of the triangle meet.

## fig. 4 orthocentre of a triangle

In the above ABC (in fig. 4), the altitudes AD, BF and CE meet at point O. This point O is the orthocentre of the ABC

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