For Exercises 1-4, make a sketch and explain how to find the answer. PART 1. The first-aid center of Mt. Thermopolis State Park needs to be at a 31 point that is equidistant from three bike paths that intersect to form a triangle. Locate this point so that in an emergency, medical A and for personnel will be able to get to any one of the paths by the shortest illa an route possible. Which point of concurrency is it? ears or with or gray 2. An artist wishes to circumscribe a circle about a triangle in his latest abstract design Which point of concurrency does he need to locate? IEW 3. Rosita wants to install a circular sink in her new triangular countertop. She wants to choose the largest sink that will fit. Which point of concurrency must she locate? Explain. 4. Julian Chive wishes to center a butcher-block table at a location equidistant from the refrigerator, stove, and sink. Which point of concurrency does Julian need to locate? 5. One event at this year's Battle of the Classes will be a pie-eating contest between the sophomores, juniors, and seniors. Five members of each class will COUGARS be positioned on the football field at the COUGARS points indicated at right. At the whistle, one student from each class will run to the pie table, eat exactly one pie, and run back to his or her group. The next 10 student will then repeat the process. The first class to eat five pies and return to home base will be the winner of the pie-eating contest. Where should the pie table be located so that it will be a fair contest? Describe how the contest planners should find that point. Construction For Exercises 6-12, construct a figure with the given specifications. 6. Given: Construct: An isosceles right triangle with z as the length of each of the two congruent sides 7. Given: R Construct: ARAP with median PM and angle bisector RB 8. Given: Construct: AMSE with OU, where O is the midpoint of MS and U is the midpoint of SE