Which of the following statements are always true? choose all that apply.

The correct statements are:

Step-by-step explanation:

1st - If the circumcenter of a triangle lies on the triangle, then the triangle is a right triangle.

The two legs of right angled triangle meet at the vertex. Now if we draw  perpendicular from the vertex to the hypotenuse. we will get the circumcenter of right angled triangle.

2nd - The incenter of a triangle is equidistant from all three vertices.

The incenter of a triangle is the point on the interior of the triangle that is equidistant from all sides.

3rd - The incenter of a triangle always lies within the triangle.