The triangle of maximum area inscribed in a circle is -

If a unit circle $S \equiv x^2+y^2+2gx+2fy+c=0$ touches the circle $S^{\prime} \equiv x^2+y^2-6x+6y+2=0$ externally at the point $P(-1, -3)$,then $g+f+c=$

Which of the following statements are true and which are false? In each case,give a valid reason for your answer.
$p:$ Each radius of a circle is a chord of the circle.

Observe the following statements:
$I$. The circle $x^2+y^2-6x-4y-7=0$ touches the $y$-axis.
$II$. The circle $x^2+y^2+6x+4y-7=0$ touches the $x$-axis.
Which of the following is a correct statement?

Find the minimum and maximum distance from the point $(6, 8)$ to the circle $x^2 + y^2 = 4$.

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