Chords PQ and RS of a circle meet at X inside the circle. If RS = 38, PX = 6, and QX = 12, then what is the smallest possible value of RX?

To answer this question, always remember that the products of the segments of the chords that intersect are always equal. For this case, the product of PX and QX is 72. Letting RX equal x we generate an equation,

(38 - x) (x) = 72.

Solving for the value of x gives us 2 and 36. Thus, the smallest possible value of RX is 2.