If from the origin two tangents are drawn to the circle $(x - 2)^2 + y^2 = 1$,then the length of the chord of contact is-

The length of the common chord of the two circles $x^2+y^2-4y=0$ and $x^2+y^2-8x-4y+11=0$ is

The length of the common chord of the circles $(x - a)^{2} + y^{2} = c^{2}$ and $x^{2} + (y - b)^{2} = c^{2}$ is .....

If the chord of contact of tangents from a point on the circle $x^2+y^2=r_1^2$ to the circle $x^2+y^2=r_2^2$ touches the circle $x^2+y^2=r_3^2$,then $r_1, r_2, r_3$ are in:

$C_1$ is the circle with centre at $O(0,0)$ and radius $4$,$C_2$ is a variable circle with centre at $(\alpha, \beta)$ and radius $5$. If the common chord of $C_1$ and $C_2$ has slope $\frac{3}{4}$ and is of maximum length,then one of the possible values of $\alpha+\beta$ is

The area of the triangle (in sq. units) formed by the tangents drawn from $P(4,4)$ to the circle $S \equiv x^2+y^2-2x-2y-7=0$ and the chord of contact of $P$ with respect to $S=0$ is