Question

A rectangle of maximum area is inscribed in the circle $|z-3-4i|=1$. If one vertex of the rectangle is $4+4i,$ then another adjacent vertex of this rectangle can be

• A. $2+4i$
• B. $3+5i$
• C. $3+3i$
• D. $3-3i$

Answer 1

Answer: (B), (C)

$3+3i$


For area to be maximum the inscribed rectangle has to a square. Let the adjacent vertex be $z.$
Then $\frac{3+4i-z}{(3+4i)-(4+4i)}=e^{\pm i\frac{\pi }{2}}$
(By rotation about center)
$3+4i-z=\pm i(-1)$
$z=3+5i\text{or}3+3i$