The triangle of maximum area inscribed in a circle is -

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

Let a circle $C_1 \equiv x^2 + y^2 - 4x + 6y + 1 = 0$ and circle $C_2$ be such that its centre is the image of the centre of $C_1$ about the $x$-axis and the radius of $C_2$ is equal to the radius of $C_1$. Then,the area of $C_1$ which is not common with $C_2$ is:

If $Q(h, k)$ is the inverse point of the point $P(1, 2)$ with respect to the circle $x^2+y^2-4x+1=0$,then $2h+k=$

If two distinct chords,drawn from the point $(p, q)$ on the circle ${x^2} + {y^2} = px + qy$ (where $pq \neq 0$),are bisected by the $x$-axis,then:

The number of tangents which can be drawn from the point $(-1, 2)$ to the circle $x^2 + y^2 + 2x - 4y + 4 = 0$ is