Tag: tangents and intersecting chords

A tangent from $P$, a point in the exterior of a circle touches circle at $Q$. If $OP=13$, $PQ=5$, then the diameter of the circle is ______________

Tangents $TP$ and $TQ$ are drawn from a point $T$ to circle $x^{2}+y^{2}=a^{2}$. If the point $T$ lies on the line $px+qy=r$, then locus of the centre of circumcircle of $\triangle TPQ$ is

Tangents PA and PB are drawn to the cicle $S\, \equiv \,{x^2}\, + \,{y^2}\, - \,2y\, - \,3\, = \,0$ from the point $P(3, 4)$. Which of the following alternative(s) is/are correct ?

If $OA$ and $OB$ are the tangents to the circle ${x}^{2}+{y}^{2}-6x-8y+21=0$ drawn from the origin $O$, then $AB$ equals 

If 't$ _{1}$','t$ _{2}$','t$ _{3}$'are the lengths of the tangents drawnfrom centre of ex-circle to the circum circle of the $ \Delta A B C $, then- $ \frac { 1 } { t _ { 1 } ^ { 2 } } + \frac { 1 } { t _ { 2 } ^ { 2 } } + \frac { 1 } { t _ { 3 } ^ { 2 } } = $

Consider a circle $x^2+y^2=3$. Secants are drawn from (-2,0) to the circle which make an intercept of $2\sqrt{2}$ units on the circle. Identify the correct statements ?

From a point P outside of a circle with center at O, tangent segments $PA$ and $PB$ are drawn. If $ \dfrac { 1 }{ \left( { OA }^{ 2 } \right)  } +\dfrac { 1 }{ \left( { PA }^{ 2 } \right)  } =\dfrac { 1 }{ 16 } $ then the length of the chord AB is ..

Parallelogram circumscribing a circle is a ?

$y=mx+b$ is a tangent to the circle ${x}^{2}+{y}^{2}-6x=16\ if\ \left (3\ m+b\right)^{2}=5\left (1+{m}^{2}\right)$.

Let  $ABCD$  be a quadrilateral in which $A B | C D , A B \perp A D \text { and } A B = 3 C D$. The area of quadrilateral  $ABCD$  is  $4.$  The radius of a Circle touching all the sides of quadrilateral is = ?