The perpendicular bisectors of a triangle intersect at a point that is always/sometimes/nnever equidistant from the midpoints off the sides of the triangle

The answer is always equidistant from the sides.

The three bisectors of the interior angles of a triangle intersect at a single point, which is always equidistant from the sides. This point is called the incenter of the triangle and is the center of the inscribed circumference of the triangle. This circumference is tangent to each side of the triangle.

Step-by-step explanation:

The bisectors of a triangle are the bisectors of its angles. The three bisectors intersect at a point called the Incenter. It can be seen that the bisector has the property that its points are at the same distance from the sides of the angle at which it divides.