If $a=3, b=5, c=7$ are the sides of a $\triangle A B C$, then $\cot A+\cot B+\cot C=$

Let $p_1, p_2$ and $p_3$ be the altitudes of a $\triangle A B C$ drawn through the vertices $A, B$ and $C$ respectively. If $r_1=4$, $r_2=6, r_3=12$ are the ex-radii of $\triangle A B C$, then $\frac{1}{p_1^2}+\frac{1}{p_2^2}+\frac{1}{p_3^2}=$

If $a=3, b=5, c=7$ are the sides of a $\triangle A B C$, then its circumradius is

Two ships leave a port at the same time. One of them move in the direction of $E 50^{\circ} \mathrm{N}$ with a speed of 8 kmph and the other moves in the direction of $\mathrm{S} 20^{\circ} \mathrm{E}$ with a speed of 12 kmph . Then, the distance between the ships at the end of 2 h is (in km )