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The bisectors of the angles of a triangle are concurrent at a point called the incentre which is also the centre of the inscribed circle that touches all three sides.
The centroid or centre of gravity. It will also be the point where the bisectors of the angles, and the perpendicular bisectors of the sides meet.
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.
inside the triangle ;) hope this helps!!
1. Opposite angles congruent 2. All sides are congruent 3. The diagonals are perpendicular bisectors of each other 4. Diagonals bisect the angles NOTE: Four congruent right triangles are formed with the right angles It has all of the properties of a parallelogram and a kite