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