Question

Three towns are linked by three straight roads. Loretta Adman has created a three-sided billboard that she wants to position as close as possible to all three roads. To do this, she needs to find the [Blank] of the triangle formed by the three roads.

Fill in the blank with:
A) Center
B) Incenter
C) Circumcenter

Answer 1

The answer is C) Circumcenter. The circumcenter of a triangle is the center of the circle that circumscribes the triangle.

Step-by-step explanation:

The circumcenter of a triangle is the center of the circle that circumscribes the triangle. In this scenario, the three towns are represented by the three roads, and Loretta Adman wants to position her billboard as close as possible to all three roads. To achieve this, she needs to find the circumcenter of the triangle formed by the three roads.

The circumcenter is equidistant from the three vertices of the triangle. By finding the circumcenter, Loretta can place her billboard as close as possible to all three roads.

To position a billboard as close as possible to all three roads, Loretta Adman needs to find the Incenter of the triangle formed by the three roads. The Incenter is the point where the angle bisectors of each angle in a triangle intersect, and it is equidistant from the sides of the triangle. Therefore, placing the billboard at the Incenter would ensure that it is as close as possible to all three roads.

The answer is C) Circumcenter.