Problem statement: Circle's point M is away from tangents A and B by 4 and 9 cm. Find how far away M is from a line AB.
My attempt: First I have drawn out the problem. Denoted x as the value that I need to find: 
I know only a few facts about inscribed triangles and one of them is the formula $S=\frac{abc}{4r}$. However it does not seem to be useful in this case as I don't really need a, b, c, r, nor S. I don't have the needed information to find them as well.
One thought that occurred to me was that I might accomplish something by searching for angles and then using sines' theorem. Problem - I don't know where to start.
Another idea that I got was to look at the fact that the problem points out how A and B are tangent lines. So, they make up right angle with the radius. Not sure where to go from there...
In the corrected figure (see @Mercy King above), with MC = 4 perpendicular to the tangent at A, and MD= 9 perpendicular to the tangent at B, join MA and MB, and draw ME perpendicular to AB. Since triangles ACM and MEB are similar (see Euclid, Elements III, 32), $4/AM = ME/MB$. And since triangles AME and BMD are likewise similar, $AM/ME = MB/9$. Therefore, $4/ME = ME/9$, making $ME^2 = 36$ and $ME = 6$.