For the circle $x ^ { 2 } + y ^ { 2 } = t ^ { 2 }$, find the value of $r$ for which the area enclosed by the tangents drawn from the point $\mathrm { P } ( 6,8 )$ to the circle and the chord of contact is maximum.
Let $A , B$, and $C$ be three events and $\bar { A } , \bar { B }$ and $\bar { C }$ be their corresponding complementary events. If the probabilities of the events $B , A \cap B \cap \bar { C }$ and $\bar { A } \cap B \cap \bar { C }$ are $\frac { 3 } { 4 } , \frac { 1 } { 3 }$ and $\frac { 1 } { 3 }$ respectively, then the eprobability of the event $B \cap C$ is
For the circle $x ^ { 2 } + y ^ { 2 } = t ^ { 2 }$, find the value of $r$ for which the area enclosed by the tangents drawn from the point $\mathrm { P } ( 6,8 )$ to the circle and the chord of contact is maximum.