Equation of sphere question

I have to find the equation of the sphere that satisfies the following:

It has it's center in the first octant and is tangent to each of the three coordinate planes. Also, the distance from the origin to the sphere is 3-√(3).

I understand 3 - √3 is a little bigger than the radius, but how do I go about finding the radius? What about the center as well?

Since sphere is tangent to each of the coordinate plane, then centre of sphere is equally distant from each coordinate plane. Therefore, centre of sphere has coordinates (a, a, a), a > 0

Distance from point (a, a, a) to each coordinate plane = a

Distance from centre of sphere to origin
= √(a²+a²+a²) = √(3a²) = a√3

Distance from origin to sphere + radius = a√3
Distance from origin to sphere = a√3 - a
3 - √3 = a√3 - a
a (√3 - 1) = 3 - √3
a (√3 - 1) = √3 (√3 - 1)
a = √3

So centre of sphere is (√3, √3, √3) and radius = √3

Equation of sphere:
(x - √3)² + (y - √3)² + (z - √3)² = 3

-- Ματπmφm --

The center coordinates must be of the form (a,a,a). It's distance to origin is sqrt(3) a.

sqrt(3) a = 3 - sqrt(3) ==> a = sqrt(3) - 1.

The sphere equation is || r - (a,a,a) || = a^2