The shortest distance of the point (9,12) from the circle x^2+y^2=16 is

The point lies outside the circle, at distance $\sqrt{81+144}=15$ from the centre $(0,0)$. The shortest distance to the circle is along the line through the centre: $15-4=11$. Trap: 15 is the distance to the centre, 19 is the farthest distance $15+4$, and 5 results from subtracting a radius of 10 instead of 4.