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

Modern Puzzles by Henry Ernest Dudeney: $116$

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?

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.

1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Geometrical Problems: Dissection Puzzles: $116$. -- The Crescent and the Star
1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Geometrical Problems: Dissection Puzzles: $339$. The Crescent and the Star