Your school has decided to produce the musical play, Porgy and Bess. All of the actors have been selected, and rehearsals are well underway. Now, the director and stage manager are trying to put together the production team, which includes the people in charge of directing lights to particular areas of the stage during each scene.

While working on a previous play, the director learned that lighting technicians with a solid understanding of geometry seemed better at the job than those without that background. Consequently, the director has asked your geometry teacher to recommend some students to serve on the stage crew. It's not a paying job, but it would look great on a college application, so you decide to see what you can do.

First, the director wants to set up the spotlights for the opening scene, when two of the characters, Jasbo and Clara, will appear on opposite ends of the stage, equidistant from center stage. Other characters will be on stage in between Jasbo and Clara, but the audience is not supposed to notice the other characters initially. To focus the audience's attention solidly on Jasbo and Clara, the two actors will be illuminated by two separate spotlights. Each spotlight can emit a circle of light up to 6 feet wide.

The director is uncertain about the number of background characters he should place on the stage in between the two featured characters. He's also not sure how wide a circle the spotlight should cast around each of the featured characters. To help him make these decisions, the director asks you to model the scene using your geometry skills.

From center stage, the director has initially set Clara three feet stage left and four feet upstage. (That's three feet left of center stage and four feet "above" center stage.)