Complex Numbers Circle Collinearity

Let C be the circle in the complex plane with centre z0=‌

1

2

(1+3i) and radius r=1. Let z1=1+i and the complex number z2 be outside the circle C such that |z1−z0|z2−z0|=1. If z0⋅z1 and z2 are collinear, then the smaller value of |z2|2 is equal to