Solution
= Solution
At the outer tangent point, the <vis-viva equation> gives $v_a=\sqrt{\mu/r_1}\sqrt{2r_0/(r_0+r_1)}$. This is below the outer <circular Kepler orbit>'s speed $v_1=\sqrt{\mu/r_1}$. The second impulse is therefore also prograde:
$$
\boxed{\Delta v_2=\sqrt{\frac\mu{r_1}}\left(1-\sqrt{\frac{2r_0}{r_0+r_1}}\right).}
$$
It raises the <pericentre> to the outer radius, completing the circularization.