Henry Ernest Dudeney/Modern Puzzles/125 - Making a Pentagon/Solution

by : $125$

 * Making a Pentagon
 * How do you construct a regular pentagon on a given unit straight line?

's original article was unnecessarily prolix.

Solution

 * Dudeney-Modern-Puzzles-125-solution.png

Let $AB$ be the unit straight line segment.

Construct $BC$ perpendicular to $AB$ half the length of $AB$.

Draw $AC$ and produce it to $D$ such that $CD = CB$.

Then $BD$ is the radius of the circle which circumscribes a regular pentagon whose side is $1$ unit.