# 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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