Interaction between Two Circles

Two circles of radii$4 \mathrm{cm}$ and$5 \mathrm{cm}$ have centres at $\mathrm{A}$and $\mathrm{B}$respectively. They touch each other externally. Then the area of the circle having a diameter is________?

The radius of the circle, having centre at (2, 1), whose one of the chord is a diameter of the circle ${\text{x}}^2+{\text{y}}^2-2\text{x}-6\text{y}+6=0$

If the circle  $C_1:x^2+y^2=16$ intersects another circle $C_2$ of radius $5$ in such a manner that the common chord is of maximum length and has a slope equal to  $\frac{3}{4}$ , then the coordinates of the centre of $C_2$ are

Two circles of radius $\sqrt{3},1$ cut each other orthogonally then area (in sq. unit) of common region is

Find the number of common tangents to the circles $x^2+y^2=1$, and $x^2+y^2-6x-8y-24=0$.

When two circles neither touch nor intersect and one lies outside the other as shown above, the number of common tangents that can be drawn is

The number of common tangents that can be drawn for two externally touching circles is

Two circles intersect in two real and distinct points as shown below, the number of common tangents that can be drawn to the circles is

When two circles touch each other internally, the number of common tangent that can be drawn to the circles is

There are two circles with centres $C_1$ and $C_2$. The radius of the circle $C_2$ is $2 \mathrm{cm}$. Distance between their centres is $15 \mathrm{cm}$. And the length of the transverse common tangent is $14 \mathrm{cm}$. Find the radius of the circle $C_1$.

There are two circles with centres $C_1$ and $C_2$. The radius of the circle $C_1$ is $3 \mathrm{cm}$. Distance between their centres is $10 \mathrm{cm}$. And the length of the transverse common tangent is $5\sqrt{3} \mathrm{cm}$. Find the radius of the circle $C_2$.

There are two circles with centres $C_1$ and $C_2$ of radii $7 \mathrm{cm}$ and $4 \mathrm{cm}$ respectively. Distance between their centres is $12 \mathrm{cm}$. The length of the transverse common tangent is 

There are two circles with centres $C_1$ and $C_2$ of radii $3 \mathrm{cm}$ and $5 \mathrm{cm}$ respectively. Distance between their centres is $9 \mathrm{cm}$. The length of the transverse common tangent is 

Check whether the given two circles touch each other, do not touch each other or intersect each other by making a quadratic equation

$x^2+5x+y^2-4y-9=0$

$x^2+4x+y^2-3y-7=0$

Check whether the given two circles touch each other, do not touch each other or intersect each other by making a quadratic equation

$x^2+4x+y^2+3y+8=0$

$x^2+3x+y^2+4y+10=0$

When two circles touch each other internally, the number of common tangents that can be drawn is 

Check whether the given two circles touch each other, do not touch each other or intersect each other by making a quadratic equation

$x^2-4x+4+y^2-6y+9=9$

$x^2-2x+1+y^2+2y+1=16$

Find the point of intersection of transverse tangents drawn to the circles having centre $c_1(2,1), c_2(3,4)$ and having radii $2,1$ respectively.

Find the point of intersection of transverse tangents drawn to the circles having centre $c_1(2,2), c_2(-2,-2)$ and having radii $2,2$ respectively.

Find the point of intersection of transverse tangents drawn to the circles having centre $c_1(3,5), c_2(-2,-3)$ and having radii $2,3$ respectively.