9. In coordinate space, three spheres of radius 1 are placed on the $xy$-plane and are mutually tangent to each other. Let their centers be $A, B, C$ respectively. A fourth sphere of radius 1 is placed above these three spheres and is tangent to all three spheres, maintaining stability. Let the center of the fourth sphere be $P$. Which of the following options are correct? (1) The plane containing points $A, B, C$ is parallel to the $xy$-plane (2) Triangle $ABC$ is an equilateral triangle (3) Triangle $PAB$ has one side of length $\sqrt{2}$ (4) The distance from point $P$ to line $AB$ is $\sqrt{3}$ (5) The distance from point $P$ to the $xy$-plane is $1 + \sqrt{3}$
9. In coordinate space, three spheres of radius 1 are placed on the $xy$-plane and are mutually tangent to each other. Let their centers be $A, B, C$ respectively. A fourth sphere of radius 1 is placed above these three spheres and is tangent to all three spheres, maintaining stability. Let the center of the fourth sphere be $P$. Which of the following options are correct?\\
(1) The plane containing points $A, B, C$ is parallel to the $xy$-plane\\
(2) Triangle $ABC$ is an equilateral triangle\\
(3) Triangle $PAB$ has one side of length $\sqrt{2}$\\
(4) The distance from point $P$ to line $AB$ is $\sqrt{3}$\\
(5) The distance from point $P$ to the $xy$-plane is $1 + \sqrt{3}$