A3. Which of the following statements is correct?

(A) The intersection of the angle bisectors of any triangle is the center of the circumcircle of that triangle.

(B) The intersection of the perpendicular bisectors of the sides of any triangle is the center of the incircle of that triangle.

(C) The centroid of any triangle coincides with the center of the incircle of that triangle.

(D) The centers of the circumcircle and the incircle of any triangle lie inside the triangle.

(E) The orthocenter of a triangle can lie outside the triangle.
A3. The intersection of the angle bisectors of a triangle is the center of the inscribed circle, the intersection of the perpendicular bisectors of the sides is the center of the circumscribed circle of the triangle, which can lie outside the triangle. The center of the circle inscribed in the triangle is not necessarily the centroid of the triangle. The orthocenter of the triangle can be outside the triangle (obtuse triangle).