It's beautiful

Geometry Level 5

3 Circles of radius 10 are tangent to each other and to a plane in 3 dimensional space. Each of the circles is inclined at \( 45^{\circ}\) to the plane. There are 3 points where the circles touch each other. These 3 points lie on a circle parallel to the plane. The radius of this circle is \(A\), evaluate \( \lfloor 10A \rfloor \).

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