2025 AIME I Problems/Problem 8
Problem
Let 
be a real number such that the system
\begin{align*}
&|25 + 20i - z| = 5 \\
&|z - 4 - k| = |z - 3i - k|
\end{align*}
has exactly one complex solution 
. The sum of all possible values of can be written as 
, where 
and 
are relatively prime positive integers. Find 
. Here 
.
