Question

1. a city planner wants to build a new library between a school, a post - office, and a hospital. draw a sketch to show where the library should be placed so it is the same distance from all three buildings. determine if this requires the circumcenter or incenter and circle the correct center below. circle the correct center. circumcenter incenter

Explanation:

Step1: Recall the properties of circumcenter and incenter

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. It is equidistant from the three vertices of the triangle. The in - center is the point where the angle bisectors of the triangle intersect. It is equidistant from the three sides of the triangle.

Step2: Determine the required center

Since the library should be equidistant from three buildings (vertices of the triangle formed by the school, post - office, and hospital), we need the circumcenter.

Answer:

Circumcenter should be circled.