The circumcenter.
The point where the perpendicular bisectors of the three sides of the triangle intersect
The point where the perpendicular bisectors of the sides of a triangle intersect is called the circumcenter. This point is equidistant from all three vertices of the triangle and serves as the center of the circumcircle, which is the circle that passes through all the vertices of the triangle.
It is the incentre.
incenter
The perpendicular bisectors of a triangle intersect at a single point called the circumcenter. This point is equidistant from all three vertices of the triangle, making it the center of the circumcircle, which is the circle that passes through all three vertices. The circumcenter's position varies depending on the type of triangle: it lies inside an acute triangle, on the hypotenuse of a right triangle, and outside an obtuse triangle.
The three ANGLE bisectors of a triangle also bisect the sides, and intersect at a point INSIDE the triangle. The angle bisectors are not necessarily perpendicular to them. The perpendicular bisectors of the sides can intersect in a point either inside or outside the triangle, depending on the shape of the triangle.
The three perpendicular bisectors (of the sides) of a triangle intersect at the circumcentre - the centre of the circle on which the three vertices of the triangle sit.
Circumcenter
The point where the perpendicular bisectors of the three sides of the triangle intersect
The point where the perpendicular bisectors of the sides of a triangle intersect is called the circumcenter. This point is equidistant from all three vertices of the triangle and serves as the center of the circumcircle, which is the circle that passes through all the vertices of the triangle.
It is the incentre.
It is the circumcentre, the unique point from which you can draw a circle (the circumscribed circle) which passes through all three vertices.
incenter
all three perpendicular bisectors elongate to meet at the incenter of the triangle.
Actually, the orthocenter of a triangle is the point where the three altitudes of the triangle intersect. The altitudes are perpendicular lines drawn from each vertex to the opposite side. The angle bisectors of a triangle intersect at the incenter, not the orthocenter.
incenter
the point where the three angle bisectors of the triangle intersect