A lady runs 12 km-towards North then 6km towards South and then 8 km East. How far is she from her starting point and in which direction?

$\mathrm{AD}=\sqrt{(\mathrm{CD})^{2}+(\mathrm{AC})^{2}}$

$=\sqrt{(8)^{2}+(6)^{2}}$

$=\sqrt{64+36}$

$=\sqrt{100}$

$=10 \mathrm{~km}$ (North-East)