What is the tangent plane equation on the 3 spheres? 3 spheres are on $z=0$ plane and touch each other as shown in the picture. Coordinates of their centers are  $O_1=(0,0,5),O_2=(0,y_2,3),O_3=(x_3,y_3,2)$. What is the tangent plane equation on 3 spheres? ($ax+by+cz=d$)

Thanks for answers.
First solve some quadratic equations to find $y_2$, $x_3$, and $y_3$.

Then, since each of the spheres is tangent to $z=0$ as well as to the mystery plane, its center must lie on the plane that bisects the angle made between these two planes. We can compute an equation for bisecting plane, because that is defined by the centers.

Now reflect the plane $z=0$ about the bisecting plane.
Isn't $z=0$ a tangent plane, by construction?