Question

Each week, Marcia travels to the office where she works, the supermarket, and a local fitness center. The three locations represent the vertices of a triangle. Marcia wants to move to an apartment that is equidistant from these three places. Where should her new apartment be located?
the center of the inscribed circle of the triangle
the center of the circumscribed circle of the triangle
the point of intersection of the angle bisectors for the triangle
the point of intersection of the perpendicular bisectors and the angle bisectors for the triangle
Done

Answer 1

The new apartment should be located in the point of intersection of the perpendicular bisectors and the angle bisectors for the triangle. This point is called CIRCUMCENTER.

The circumcenter of a triangle is a point in the plane equidistant from the three vertices of the triangle. It is the point of concurrency of the three perpendicular bisectors of each side of the triangle.

Answer 2

the center of the circumscribed circle of the triangle