NY Regents Exam   Teasers   IQ Tests   Chemistry   Biology   GK   C++   Recipes   Search <  a href="/cgi/members/home.cgi" class="toplink">Members   Sign off

Print Preview

### Math Puzzles & Brain Teasers

At a Tangent

 View Puzzle Solve Puzzle
 Hide all answers   View all answers   Print   Try the Quiz 1. Consider 11 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? Answer: 22 Solution: If there are 11 tangent lines, then there are 22 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? By induction?! 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