Let $y=x+2$,$4y=3x+6$,and $3y=4x+1$ be three tangent lines to the circle $(x-h)^2+(y-k)^2=r^2$. Then $h+k$ is equal to:

In the figure shown,the radius of circle $C_1$ is $r$ and that of $C_2$ is $\frac{r}{2}$,where $r = \frac{1}{3} PQ$. Then the length of $AB$ is (where $P$ and $Q$ are the centers of $C_1$ and $C_2$ respectively).

Find the $x$-intercept of the circle $x^2 + y^2 + 4x - 7y - 12 = 0$.

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 $2h+k=$

$A$ person $X$ is running around a circular track,completing one round every $40 \ s$. Another person $Y$ running in the opposite direction meets $X$ every $15 \ s$. The time,expressed in seconds,taken by $Y$ to complete one round is

In a rectangle $ABCD$,the coordinates of $A$ and $B$ are $(1, 2)$ and $(3, 6)$ respectively,and some diameter of the circumscribing circle of $ABCD$ has the equation $2x - y + 4 = 0$. Then,the area of the rectangle is