Amit M Agarwal Solutions for Chapter: Circle, Exercise 2: Work Book Exercise 13.2

For the two circles, $x^2+y^2=16$ and $x^2+y^2-2y=0$ there is/are

If the chords of contacts of tangents from three points $A, B, C$ to the circle $x^2+y^2=a^2$ are concurrent, then $A, B, C$ will be

If a line is drawn through a fixed point $P(\alpha ,\beta )$ to cut the circle $x^2+y^2=a^2$ at $A$ and $B,$ then $PA·PB$ is equal is

If the two conics $a_1{x}^2+2h_{1}xy+b_1{y}^2=c_1, a_2{x}^2+2h_{2}xy+b_2{y}^2=c_2$ intersect in four concyclic points, then

If the polar of a point $\left(p,q\right)$ with respect to the circle $x^2+y^2=a^2$ touches the circle ${\left(x-c\right)}^2+{\left(y-d\right)}^2=b^2,$ then

If the chord of contact of tangents from of a point $\mathrm{P}$ to a given circle passes through $\mathrm{Q}$ ,then the circle on $\mathrm{PQ}$ as diameter

If the chord of contact of tangents from a point $P$ to a circle passes through $Q.$ If $l_1$ and $l_2$ are the lengths of the tangents from $P$ and $Q$ to the circle, then $PQ$ is equal to

The circle $S_1$ with centre $C_1\left(a_1,b_1\right)$ and radius $r_1$ touches externally the circle $S_2$ with centre $C_2\left(a_2,b_2\right)$ and radius $r_2.$ If the tangent at their common point passes through the origin, then