Radius of circle with complex equation

Algebra Level 4

Find the radius of the circle with centre \(\dfrac{1}{2}(1+i)\) on which a complex number \(z\) lies such that \(\dfrac{z-i}{z-1}\) is purely imaginary.

Note: A complex number \(a\) is purely imaginary if \(a=\lambda.i\) where \(\lambda \in \mathbb{R}\).

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