Problem #4 - Applying the Points of Concurrency

The Skokie Police Department wants to open a new station in Skokie. The current Skokie Police department is stationed on Touhy and Niles Center Road but there is no police station easily accessible to Skokie Hospital, Old Orchard Shopping Center, and Weber Park. Therefore, they are looking to build a station that is equidistant from these three locations. At which intersection should they build the new station?

Red Mango would like to build a new location. They took a poll of where their customers drive from and noticed that the common intersections were Skokie Blvd and Golf,  and Church St and Skokie Blvd, and Long Road and Church St. They would like to build this new location at a point that is equidistant from both Church St and Skokie Blvd. Where should they build the new location? Is this a good location to build? Why or why not?

Gary, Danny and Shawn are looking for Tina because they want to go out for lunch.  Shawn is at the Memorial Park Cemetery, Danny is on the corner of Lawler and Lyons waiting for a bus, and Gary is on the corner of Kostner and Church canning for Relay for Life. Tina is located at the orthocenter of the triangle formed by their three locations. Where will they find Tina so they can have lunch together?

Chris is at Niles North High School, Georgia is at Old Orchard Junior High School, and Nevin is at Weber Leisure Center. The three of them want to meet at the centroid of the triangle that is formed by their three locations. Where should they meet?