if q(z) is a locus of mid points of chords of contact for tangents drawn from p(z) to ​​modulus of ​z=2 (tangents from p(z) are mutually perpendicular) then the shortest distance of q(z) from origin is??

ans=root 2 how??

 P(z) is a circle with centre origin and radius2.

 If we draw tangents such that they are mutually perp. then the point of contact of tangents also subtend an angle of 90 degree at centre. then the length of chord will be 2*root2. using pythagoras thm. we can simply find that the dist of centre of chord is root 2