The circumcentre of triangle ABC turns out to lie on the side BC itself. What can be concluded about the triangle?

The circumcentre is equidistant from all three vertices, so if it lies on BC then it is the midpoint of BC and BC is a diameter of the circumcircle. A is on that circle, and an angle in a semicircle is a right angle, so ∠BAC = 90°. This is the converse of the familiar fact that the circumcentre of a right triangle sits at the midpoint of the hypotenuse. If the angle at A were obtuse the circumcentre would fall OUTSIDE the triangle, beyond BC, not on it.