Chord of contact

Let the tangent to the circle $C_1:x^2+y^2=2$ at the point $M(-1,1)$ intersect the circle $C_2:(x-3)^2+(y-2)^2=5$, at two distinct points A and B. If the tangents to $C_2$ at the points A and B intersect at N, then the area of the triangle ANB is equal to :

Let the tangents at two points A and B on the circle $x^2+y^2-4x+3=0$ meet at origin O (0, 0). Then the area of the triangle OAB is :

Let AB be a chord of length 12 of the circle $(x-2)^2+(y+1)^2=\dfrac{169}4$. If tangents drawn to the circle at points A and B intersect at the point P, then five times the distance of point P from chord AB is equal to _______.

Let $E_1E_2$ and $F_1F_2$ be the chords of $S$ passing through the point $P_0(1, 1)$ and parallel to the x-axis and the y-axis, respectively. Let $G_1G_2$ be the chord of $S$ passing through $P_0$ and having slope $-1$. Let the tangents to $S$ at $E_1$ and $E_2$ meet at $E_3$, the tangents to $S$ at $F_1$ and $F_2$ meet at $F_3$, and the tangents to $S$ at $G_1$ and $G_2$ meet at $G_3$. Then, the points $E_3$, $F_3$, and $G_3$ lie on the curve

The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line $4x-5y=20$ to the circle $x^2+y^2=9$ is