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 ircle only constructions
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| Easier | Harder | ||
| Construct a symmetric
point Construct the equilateral triangle ABC Construct a perpendicular Construct the 60° rhombus Double the length AB Construct a regular hexagon |
Construct the midpoint of AB Construct the square ABCD Construct a square given diagonal corners Construct the bisector of an arc Construct a ratio Construct the circumcircle of ABC Construct the centre of a circle Divide a circle into quarters Construct a regular pentagon |
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Which constructions are possible using only the
circle construction tool? 
In 1797 an Italian geometer, Lorenzo Mascheroni, proved
that every compass-and-straightedge construction can be done with a compass
alone. For this reason such constructions are still called
Mascheroni constructions.