Solution to the Flag Problem

leg L

This seemingly complex problem can be simply resolved by considering extreme cases.  One extreme case of the trapezoid is when it is actually a triangle.  That is, when the top two points on the diagram above coincide.  The solution, then, is clearly the midpoint, P, of the hypotenuse shown.

leg L

Another extreme case is when the trapezoid is actually a rectangle, achieved by extending the top side of the trapezoid to become the same size as the bottom side.  In this other extreme case, the solution is any point on the leg opposite of leg L. Clearly, then, the midpoint of this leg, P, would work.

leg L

Since in the first extreme case the midpoint is the only solution, and in the second extreme case the midpoint is a solution, we conclude that the midpoint is the only point that works for BOTH extreme cases given. Thus, regardless of the trapezoid, the solution is that P is the midpoint of the leg opposite L.

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