There is not always the circumcentre of a triangle inside the triangle. For the triangle, therefore, the othorcentre and the circumcentre are two points of rivalry which can be found outside of the triangle.
The incentre of a triangle is the intersection of all the angle bisectors of the triangle. It is always located inside the triangle.
The centroid of a triangle is the intersection of the lines joining the midpoint of each side of the triangle with the opposite vertex. I always lies within the triangle.
The orthocenter of a triangle <span>is the point where all three altitudes of the </span>triangle<span> intersect. An </span>altitude<span> is a line which passes through a vertex of the </span>triangle<span> and is perpendicular to the opposite side. The othorcenter of the triangle does not alway lie inside the triangle.
The</span> circumcenter of a triangle<span> is the point where the perpendicular bisectors of a </span>triangle<span> intersect. The </span>circumcenter<span> is also the center of the </span>triangle's circumcircle<span> - the circle that passes through all three of the </span>triangle's<span> vertices. The circumcentre of a triangle is not always located inside the triangle.
Therefore, f</span><span>or a triangle, the two points of concurrence which could be located outside the triangle are the othorcenter and the circumcenter.</span>
