Question

given the following statement, determine to which point(s) the statement applies.
equidistant from the vertices of a triangle.

choose the correct answer below.
a. both circumcenter and incenter
b. incenter
c. circumcenter
d. neither circumcenter nor incenter

Explanation:

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides intersect. By definition, the circumcenter is equidistant from all three vertices of the triangle (this distance is the radius of the circumscribed circle around the triangle). The incenter is the point where the angle bisectors intersect and is equidistant from the sides of the triangle (not the vertices). So the point equidistant from the vertices is the circumcenter.

Answer:

C. Circumcenter