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

Modern Puzzles by Henry Ernest Dudeney: $125$

Making a Pentagon

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

Dudeney's original article was unnecessarily prolix.

Solution

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.

Proof

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Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $125$. -- Making a Pentagon
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $257$. Making a Pentagon