Question

I have a geometry question.... See more

Answer 1

Solving Problems Through Diagrams
As basketball season is gearing up, Armando wonders how many conference games will be played this year. He knows the varsity basketball team plays every other team twice this season. Since there are 7 total teams, the answer seems fairly simple. Armando conjectures that you take 7 x 6 x 2 = 84 games. After all, there are 7 teams playing 6 other teams twice. Yet this just seems like more games than is possible to Armando. He decides to draw a diagram of seven noncollinear points in a circle to represent the seven teams and labels the points A through G. He connects point A to the six remaining points, point B to the remaining 5, point C to the remaining 4, etc.

Answer 2

When all points are connected, Armando determines there are 6 + 5 + 4 + 3 + 2 + 1, or 21 segments. He counts them just to be sure. Since all the teams play each other twice, there will be 2 x 21, or 42 games this season. His conjecture was incorrect; there will be 42, not 84 games.
Now it's your turn.
You're standing in a large circle in gym class. As everyone counts off by 1's, you notice your number (9) is exactly opposite your best friend (25). Assuming everyone is evenly spaced around the circle, how many total students are in class today? (