Question

If the radius of the circumcircle of the triangle TPQ, where PQ is chord of contact corresponding to point T with respect to circle $x^2+y^2-2x+4y-11=0$, is $12$ units, then minimum distance of $T$ from the director circle of the given circle is

• A. $6$
• B. $12$
• C. $6\sqrt{2}$
• D. $12-4\sqrt{2}$

Answer 1

Answer: (D)

$12-4\sqrt{2}$

Given circle $(x-1{)}^2+(y+2{)}^2=16$
Its director circle is $(x-1{)}^2+(y+2{)}^2=32$
$\Rightarrow$ $OS=4\sqrt{2}$
Therefore, required distance, $TS=OT-SO=12-4\sqrt{2}$