Henry Ernest Dudeney/Modern Puzzles/116 - The Crescent and the Star

by : $116$

 * The Crescent and the Star
 * Here is a little puzzle on the Crescent and the Star.
 * Look at the illustration, and see if you can determine which is the larger, the Crescent or the Star.
 * If both were cut out of a sheet of solid gold, which would be more valuable?


 * Dudeney-Modern-Puzzles-116.png


 * As it is very difficult to guess by the eye,
 * I will state that the outer arc is a semicircle;
 * the radius of the inner arc is equal to the straight line $BC$;
 * the distance in a straight line from $A$ to $B$ is $12$ units,
 * and the point of the star, $D$, contains $3$ square units.


 * Now it is quite easy to settle the matter at a glance -- when you know how.