Henry Ernest Dudeney/Modern Puzzles/139 - A Crease Problem/Solution

by : $139$

 * A Crease Problem
 * Fold a page, so that the bottom outside corner touches the inside edge and the crease is the shortest possible.


 * That is about as simple a question as we could put,
 * but it will puzzle a good many readers to discover just where to make the fold.
 * I give two examples of folding.
 * It will be seen that the crease $AB$ is considerably longer than $CD$, but the latter is not the shortest possible.


 * Dudeney-Modern-Puzzles-139.png

Solution

 * Dudeney-Modern-Puzzles-139-solution.png

Bisect $AB$ at $C$ and construct $CG$ parallel to $BH$.

Bisect $AC$ at $D$ and construct the semicircle between $B$ and $D$.

Let the semicircle $BD$ intersect $CG$ at $E$.

Let $DE$ be produced to intersect $BH$ at $F$.

Then $DF$ is the required crease.