The chord of contact of the tangents drawn from a point on the circle $x^2 + y^2 = a^2$ to the circle $x^2 + y^2 = b^2$ touches the circle $x^2 + y^2 = c^2$. Then $a, b, c$ are in:

The equation of a common tangent to the circle $x^2+y^2=16$ and the ellipse $\frac{x^2}{49}+\frac{y^2}{4}=1$ is

$A$ tangent $PT$ is drawn to the circle $x^2+y^2=4$ at the point $P(\sqrt{3}, 1)$. If a straight line $L$ which is perpendicular to $PT$ is a tangent to the circle $(x-3)^2+y^2=1$,then a possible equation of $L$ is

$ABCD$ is a square with side length $a$. Taking $AB$ and $AD$ as the coordinate axes,find the equation of the circle passing through the vertices of the square.

In a right triangle $ABC$,right-angled at $A$,a semicircle is described on the leg $AC$ as diameter. If $D$ is the point of intersection of the hypotenuse $BC$ and the semicircle,then the length $AC$ is equal to:

$A$ pair of tangents are drawn to a unit circle with centre at the origin and these tangents intersect at a point $A$ enclosing an angle of $60^o$. The area enclosed by these tangents and the arc of the circle is