Pair of Tangents

The area of the triangle formed by the tangents from the point $(4, 3)$ to the circle $x^2+y^2=9$ and the line joining their points of contact is

The angle between the two tangents drawn from origin to the circle $x^2+y^2-14x+2y+25=0$ is $\_\_\_\_\_\_\_\_\_$

Let $A$ be the centre of the circle $x^2+y^2-2x-4y-20=0,$ and $B\left(1,7\right)$ and $D(4,-2)$ are points on the circle then, if tangents be drawn at $B$ and $D$, which meet at $C$, then area of quadrilateral $ABCD$ is

Let $T$ be a circle with diameter $AB$ and centre $O$. Let $l$ be the tangent to $T$ at $B$. For each point $M$ on $T$ different from $A$, consider the tangent $t$ at $M$ and let interest $l$ at $P.$ Draw a line parallel to $AB$ through $P$ intersecting $OM$ at $Q.$ The locus of $Q$ as $M$ varies over $T$ is

What will be the area of the quadrilateral $OACB$ formed by the joining of tangents $OA$ and $OB$from the origin to the circle having equation $x^2+y^2+2gx+2fy+c=0$ ,and $C$ be the centre of the circle ?

Two tangents are drawn from the circle $x^2+y^2=r^2 {\sin }^2 \alpha \left(0<\alpha <\frac{\pi }{2}\right)$, and a concentric circle passing through the point of intersection of the tangents has the equation $x^2+y^2=r^2$. The angle between the tangents is-

The circumcentre of the triangle $OPQ$ formed by $\mathrm{O}$ as the origin and $\mathrm{O}\mathrm{P}$ , $\mathrm{O}\mathrm{Q}$ as distinct tangents to the circle ${\mathrm{x}}^2+{\mathrm{y}}^2+2\mathrm{g}\mathrm{x}+2\mathrm{f}\mathrm{y}+\mathrm{c}=0$ is:

The locus of the point of intersection of tangents to the circle x = a cosθ, y = a sinθ at a point whose parametric angles differ by π/3 is x² + y² = ka². Find the value of 3k.

The range of values of $\mathrm{\prime }\mathrm{a}\mathrm{\prime }$ such that the angle $\mathrm{\theta }$ between the pair of tangents drawn from $\left(\mathrm{a},\mathrm{ }0\right)$ to the circle ${\mathrm{x}}^2+{\mathrm{y}}^2=1$ satisfies $\frac{\mathrm{\pi }}{2}<\mathrm{\theta }\mathrm{ }<\mathrm{\pi }$ , lies in

Tangents drawn from origin to the circle ${\mathrm{x}}^2+{\mathrm{y}}^2\mathrm{ }–2\mathrm{p}\mathrm{x}\mathrm{ }–2\mathrm{q}\mathrm{y}+{\mathrm{r}}^2=0$ are perpendicular if

Let $PQ$ and $RS$ be tangents at the extremities of the diameter $PR$ of a circle of radius $r$. If $PS$ and $RQ$ intersect at a point $x$ on the circumference of the circle, then $2r$ equals

Angle between tangent drawn to circle $x^2+y^2=20$, from the point $\left(6, 2\right)$ is

The locus of the point intersection of the tangent to the circle $x^2+y^2=a^2$, which include an angle of $45°$ is the curve ${\left(x^2+y^2\right)}^2=\lambda a^2\left(x^2+y^2-a^2\right)$. The value of $\lambda$  is

If $x=3$ is the chord of contact of the circle $x^2+y^2=81$, then the equation of the corresponding pair of tangents is

The angle between the tangents from the origin to the circle (x - 7)² + (y + 1)² = 25 is

The angle between the tangents drawn from origin to the circle ${\left(x-7\right)}^2+{\left(y+1\right)}^2=25$ is