Find the radius of the circle in which a central angle of $60^{\circ}$ intercepts an arc of length $37.4 \, cm$ (use $\pi = \frac{22}{7}$). (in $cm$)

The line $y=mx+c$ intercepts the circle $x^2+y^2=r^2$ in two distinct points,if

If $P(\frac{\pi}{3})$ and $Q(\frac{2\pi}{3})$ represent two points on the circle $x^2+y^2-4x+6y-12=0$ in parametric form,then the length of the chord $PQ$ is

Find the area of a circle that passes through the point $(4, 6)$ and has its center at $(1, 2)$. (in $\pi$)

If the angle between the circles $x^2+y^2-2x-4y+c=0$ and $x^2+y^2-4x-2y+4=0$ is $60^{\circ}$,then $c=$

Let a circle $C: (x-h)^{2} + (y-k)^{2} = r^{2}, k > 0$,touch the $x$-axis at $(1, 0)$. If the line $x + y = 0$ intersects the circle $C$ at $P$ and $Q$ such that the length of the chord $PQ$ is $2$,then the value of $h + k + r$ is equal to