1956 AHSME Problems/Problem 35
Solution
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