Let X be a point obviously outside the figure. Draw . How many times does it cross the curve?
A) it will cross the curve an odd number of times
B) it will cross the curve an even number of times

Question

Let X be a point obviously outside the figure. Draw  . How many times does it cross the curve? ​  ​
A) it will cross the curve an odd number of times 
B) it will cross the curve an even number of times

Quizplus · Accepted Answer

Since the point X is outside the figure and the curve enclosing the figure is a closed loop, any line drawn from X to infinity must cross the curve an odd number of times, by the Jordan Curve Theorem. Therefore, the answer is A, it will cross the curve an odd number of times.

Let X Be a Point Obviously Outside the Figure