in a circle circumscribed about a triangle, the distance from any vertex to the circumcenter is?

The distance from any vertex of a triangle to the circumcenter (the point where the perpendicular bisectors of the sides of the triangle intersect) is equal to the radius of the circumcircle (the circle circumscribed about the triangle).

Therefore, the distance from any vertex to the circumcenter is equal to the radius of the circumcircle.