Circles, Chords, and Polygons - March 13-17, 1995 "Dolores! You look like a zombie!" "Thanks a lot, Noel. I had this dream last night about this problem I was working on after dinner." "Tell me about it. Maybe I can give you a hand," said Noel helpfully. "Okay. In the first part, you have a circle with a chord drawn. You have to prove that the perpendicular bisector of the chord goes through the center of the circle." "That doesn't sound too bad," said Noel. "What's the part that kept you up all night?" "After we prove that first part, we're supposed to use that somehow to show how to decide if, given a polygon, you can circumscribe a circle around that polygon." "Okay, so you're saying that we don't know if we can put a circle around this polygon?" asked Noel. "Right," said Dolores. "And circumscribe means that the circle has to go around the polygon and touch all the vertices." "You got it. So how can we use the first part to figure out an answer to the second part? How can we decide whether we can circumscribe a circle around some random polygon?" "Wow, no wonder you look like a zombie this morning. Let's not linger - this seems tough!" "Great! I want to see if we can get the second part by the end of the week." Correct solutions to the problem were submitted by: Sean Nichols, Burnaby South Secondary School Samantha Brenner, Fairfield HS Next problem || Previous problem || Table of Contents || Forum Home Page