Home > Math Puzzles & Brain Teasers > Print Preview
Math Puzzles & Brain Teasers
At a Tangent
Hide all answers
View all answers
Try the Quiz
1. Consider 39 lines drawn at a tangent to an ellipse. The lines break up the plane into several regions, some bounded (i.e., enclosed) and others unbounded. How many unbounded regions are there?
If there are 39 tangent lines, then there are 78 unbounded regions.
It is not very difficult to visualize that each tangent line drawn creates two unbounded regions.
The animation shows 3 tangent lines. The unbounded regions are in yellow and the bounded regions in green.
For 3 tangent lines, there are 6 unbounded regions.
Food for thought:
How do you arrive at the solution to such a problem?
Try to solve the problem for 1 tangent line, 2 tangent lines, and so on. It is easy to then generalize.
Try the Quiz : Puzzles & Brain Teasers : At a Tangent