Oscar purchased land on which to build a campground. Use your geometry skills to help Oscar make decisions as he sets up his camp. 1.) The building plan contains a central area with a pool, playground, and basketball courts, as shown. Oscar plans to build a bathroom that is equidistant from the basketball courts, the playground, and the pool.

a.) Which point of concurrency of a triangle should Oscar use to determine the location of the bathroom? Explain your reasoning.

b.) Use a construction to determine the location of the bathroom. Do not erase any construction marks.

In another part of the campground, while Oscar was digging he found some archeological artifacts. He thinks that he might have found a part of a Roman coin. He emails an archaeologist to discover what type of coin he found. During the first two centuries of the Roman Empire there were many different denominations and sizes of coins. In order to identify the coin, it is necessary to determine the diameter of the coin. The archaeologist explains that you must, “Construct two chords on the coin, then construct the perpendicular bisectors of the chords.” The email seems incomplete.

Help Oscar perform the steps and answer his questions.

b.)Construct two chords on the coin.
What is a chord?

c.) Do the chords need to be congruent?

d.) Can the chords intersect?

e.) Construct the perpendicular bisector of the chords.

That night Oscar took a break and gazed up into the sky. He noticed that there are many satellites that orbit the Earth. He began wondering about the distance some of these satellites are from the Earth. Satellite A orbits closer to Earth than Satellite B. At one point in their orbits, the distance from Satellite A to Satellite B is 21,185.5 kilometers. Their distances from each other and the center of the Earth form a triangle as shown.

For all calculations, assume:

• The radius of the Earth is 6371 kilometers.

• All satellites have a circular orbit.

• All related measurements lie on
the same plane.

a.) Determine the distance Satellite
B is from the Earth. Show your work.

b.) Show two different methods for determining the distance Satellite A is from the Earth.