Two tangents $\overline{PA}$ and $\overline{PB}$ are drawn to a circle, where $P$ lies outside the circle, and $A$ and $B$ lie on the circle. The length of $\overline{PA}$ is $3,$ and $AB$ has a length of 8. Find the radius of the circle.
If we look at triangle BPA....note that BP = AP = 3 and AB = 8
But BP + AP < AB which, by the triangle inequality, is impossible