Length of Chord of Contact

Q. Qonsider a family of circles passing through the point { of intersection of the lines \sqrt3(y-1)=x-1 and y-1{=\sqrt3(x-1) and having its centre on the acute angle bisector of the given lines. Then the common chords of { each member of the family and the circle x^2+y^2+4x-{6y+5=0 are concurrent at

Q. In the given figure, two circles of different radii are placed against a right angle. If the radius of the bigger circle is 1 unit, then the radius of the smaller circle is

1. 
   $3-2\sqrt{2}units$
2. 
   $6-4\sqrt{2}units$
3. 
   $5-2\sqrt{2}units$
4. 
   $3-4\sqrt{2}units$

Q. The tangents are drawn from origin and the point $(g,f)$ to the circle $x^2+y^2+2gx+2fy+c=0$. Find the distance between chords of contact.

1. $\frac{2(g^2+f^2-c)}{\sqrt{g^2+f^2}}$
2. $\frac{g^2+f^2-c}{\sqrt{g^2+f^2}}$
3. none of these
4. $\frac{g^2+f^2-c}{2\sqrt{g^2+f^2}}$

Q.

Tangents are drawn from (4, 4) to the circle $x^2+y^2-2x-2y-7=0$ to meet the circle at A and B. The length of the chord AB is

1. $3\sqrt{2}$

2. $2\sqrt{3}$

3. $2\sqrt{6}$

4. $6\sqrt{2}$