Let z₀ be the complex number satisfying |z - (1+2i)| = |z - (5+2i)| = |z - (1+8i)| . The value of |z₀ - 1|^2 is equal to:

Step-by-step solution

The given equations imply that z₀ is equidistant from the points A(1, 2) , B(5, 2) , and C(1, 8) in the complex plane. The point z₀ is the circumcenter of the triangle ABC . Notice that the line segment AB is horizontal (parallel to the real axis) and the line segment AC is vertical (parallel to the imaginary axis). Therefore, ABC is a right-angled triangle with the right angle at vertex A . In a right-angled triangle, the circumcenter is the midpoint of the hypotenuse. The hypotenuse is the line segment joining B(