The correct option is C √(a+¯¯¯a)2−4r
Points where the circle cuts the x−axis z=¯¯¯z.
Hence subsituting z=¯¯¯z in the equation of circle, we get
z2+¯¯¯az+az+r=0
⇒z2+(a+¯¯¯a)z+r=0
⇒AB=|z1−z2|
(where A and B are points of intersectoin of circle with x− axis)
=√(z1+z2)2−4z1z2
=√(a+¯¯¯a)2−4r