Length of Tangent and Power of a Point

Q. Length of tangent drawn from any point of circle $x^2+y^2+2gx+2fy+c=0$ to the circle $x^2+y^2+2gx+2fy+d=0$, (d > c) is

1. $\sqrt{c-d}$
2. $\sqrt{d-c}$
3. $\sqrt{f-g}$
4. $\sqrt{g-f}$

Q. ABD and ACE are the two tangents to the circle having centre O, then AB + AC equals ______ of triangle AMN.

1. 2s
2. s/2
3. 3s
4. s

Q. A point $P$ moves so that the length of the tangent from $P$ to the circle $x^2+y^2-2x-4y+1=0$ is three times the distance of $P$ from the point $(1,-2)$. Then the locus of $P$ is a straight line. Is this statement true?

Q. The number of common tangents to the circles $x^2+y^2-4x-6y-12=0$ and $x^{{}^2}+y^2+6x+18y+26=0$, is:

1. $2$
2. $3$
3. $1$
4. $4$

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

1. $\frac{ab}{\sqrt{a^2+b^2}}$
2. $\frac{2ab}{\sqrt{a^2+b^2}}$
3. $\frac{2ab}{a^2+b^2}$
4. $\frac{ab}{a+b}$

Q. ABD and ACE are the two tangents to the circle having centre O, then AB + AC equals ______ of triangle AMN.

1. 2s
2. s
3. s/2
4. 3s