Let $PQ$ and $RS$ be the tangent 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 $(PQ.RS)$ is equal to
$(PX).(RX)$
$(QX).(SX)$
$(PX)^2 + (RX)^2$
$(QX)^2 + (SX)^2$
If the lines $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ are tangents to a circle, then the radius of the circle is
The line $3x - 2y = k$ meets the circle ${x^2} + {y^2} = 4{r^2}$ at only one point, if ${k^2}$=
Equation of the tangent to the circle, at the point $(1 , -1)$ whose centre is the point of intersection of the straight lines $x - y = 1$ and $2x + y= 3$ is
A circle with centre $(a, b)$ passes through the origin. The equation of the tangent to the circle at the origin is
A circle with centre $'P'$ is tangent to negative $x$ & $y$ axis and externally tangent to a circle with centre $(-6,0)$ and radius $2$ . What is the sum of all possible radii of the circle with centre $P$ ?