1956 AHSME Problems/Problem 35
First, we create a circle and its radii. Both of these have length . When we join them, we get our first chord. Let's call this . Now, we can create two more chords of our own choice, as long as both of them start from points and respectively and our final figure looks like a rhombus. Let's call these newly created points and . Thus, now we have our rhombus . Since we known the formula for a rhombus's area is , we can now successfully substitute the and the both with (since, in our case, we had a circle, both our and are going to be the same). After substituting, we get: ; upon using arithmetic, we yield our answer to be .
-Solution by DRAGONWARRIOR123