Geometric Points of Concurrency

PREPARE FOR YOUR MISSION:  While in flight to your secret rendevous sight where you will receive your specific mission orders, please use this time to use all your current human intelligence, HUMINT, to begin listing on a piece of notebook paper all the properties about triangles and their points of concurrency (incenters, orthocenters, circumcenters, and centroids) that you already know.

TEAM UP:  Now that you have all arrived at your secret MIF safe house, please introduce yourself to your mission team members.  Find one thing everyone has in common then share your new current triangle knowledge with your MIF team members.  After combining and agreeing on your current triangle knowledge, please carefully read the summaries of the four missions.  You may complete the four missions as the MIF team in any order you wish.  However, all four mission must be completed within 72 hours.  Good Luck!

PRE-OPERATIONS INTELLIGENCE GATHERING:  While in your MIF safe house, complete the Pre-Op Mission packet.  This task will involve availabe accessing web resources to enhance your team's knowledge of points of concurrency (centroid, circumcenter, incenter, and orthocenter). 

MISSION 1 (Order FG- S-2698-M: Direct from the Smithsonian Institute in Washington, D.C.):  The Smithsonian Institute has funded an archeological dig team in Cambodia.  They have discovered significant artifacts in an early earthwork from an Early Iron Age village (middle of 1st millennium BC).  The scientists have discovered a partial circle of remains and now need your expertise.  Time, expense, and the Cambodian government will not allow the dig team to totally excavate the entire sacred Memot area.  Your mission is to assist the archeologists in finding the exact location of the actual hidden circular earthwork and its exact center. 

MISSION 2 (Order SG-GA-313-C: Direct from The Office of the Governor for the State of Georgia): Recent state revenue losses have caused a billion dollar shortfall and all state budgets must be reduced. Vital services must be cut or consolidated.  Many rural counties of Georgia will have their small medical centers and hospitals closed.  The mission is to close all hospitals in Emanuel County, Burke County, and Jefferson County and use that money to build one modern, efficient, and state-of-the-art hospital that citizens of all three counties can utilize.  Your mission is locate the best location that will be equal distances from the towns of Swainsboro, Waynesboro, and Louisville, Georgia while keeping transportation on good roads to this new hospital as a criteria.

MISSION 3 (Direct from your favorite uncle):  Okay, this may not be secret or of national importance but you did promise to help him a few days ago when he called.  Apparently your uncle is the cross-country coach at Collins Hill High School. His team is running on a triangular shaped race course this weekend and needs you to help him before the upcoming race.  His runners� parents and fans want to watch and cheer the runner on each straight part of the race course.  They also want to walk the minimum distance possible to each straightaway.  They need your help in finding the best location for them to set up their base camp to make this possible.

MISSION 4 (Order FG- NSA-76-A: Direct from The Office of the President of the United States):  A very frantic Director of National Aeronautics and Space Administration (NASA) has called President Obama from its NEO (Near Earth Object) department.  It seems that NEO has detected a 12 km triangular shaped asteroid heading on a path that will impact Earth.  Your assistance is necessary to locate the best point on the asteroid to target a single missile strike.  If the asteroid shatters into many small pieces they will burn up entering our Earth's atmosphere.  Otherwise, it will not just be dinosaurs that are extinct.

MISSION DEBRIEFING: Upon completion of all missions, the National Security Agency and Department of Homeland Security have both asked for a few personal reflections on the missions successes and difficulties.