Chords \overline{PQ} and \overline{RS} of a circle meet at $X$ inside the circle. If $RS = 38$, $PX = 38$, and $QX = 36$, then what is the smallest possible value of $RX$?
We have that
PX * QX = RX * SX
Let RX = s and SX = (38 -s)
So
38 * 36 = s * (38 -s)
1368 = 38s - s^2 rearrange as
s^2 - 38s + 1368 = 0
(This has no real solution for s !!! )
+513 
