Orthocenter
My improvement:
The three angle bisectors will intersect at a point called the incenter. At this point it also the center of the largest possible circle within the triangle. Since a circle has a center point, this point within the triangle is called the incenter.
The three heights of a triangle will meet at a special point called the orthocenter.
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The 3 angle bisectors of a triangle intersect in a point known as the INCENTER.
The three angle bisectors in a triangle always intersect in one point, and this intersection point always lies in the interior of the triangle. The intersection of the three angle bisectors forms the center of the circle in- scribed in the triangle. (The circle which is tangent to all three sides.) The angle bisectors meet at the incenter which has trilinear coordinates.
incenter of a triangle
The circumcenter, the incenter is the point of concurrency of the angle bisectors of a triangle.
Oh, what a happy little question! The type of triangle you're describing is called an equilateral triangle. In an equilateral triangle, all three angles are equal, and the angle bisectors are also the perpendicular bisectors of the sides, creating a beautiful balance in the painting of geometry.