(7) Let a fixed point $P$ outside the plane $\alpha$ be at a distance $h$ from $\alpha$, and let three moving points $A$, $B$, and $C$ on $\alpha$ be at distances $a$, $b$, and $c$ from $P$ respectively, with $\angle PBA = 90^{\circ}$. Then the maximum area of $\triangle ABC$ is $\qquad$ (expressed in terms of $a$, $b$, $c$, and $h$).
(7) $\frac{1}{2} \sqrt{a^{2}-b^{2}}\left(\sqrt{b^{2}-h^{2}}+\sqrt{c^{2}-h^{2}}\right)$ Hint: $|A B|=$ $\sqrt{a^{2}-b^{2}}$, Let the projection of $P$ on $\alpha$ be $Q, A B \perp B Q,|B Q|=\sqrt{b^{2}-h^{2}}$, $|C Q|=\sqrt{c^{2}-h^{2}} . C$ to $A B$ distance is less than or equal to $|B Q|+|C Q|$.