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Geometric Maximum Determination

Let $ a, $ $ b, $ and $ c $ be real numbers such that $ a \ge b \ge c \ge 0 $ and $ a + b = 16 $. Find the maximum value of \[\sqrt{c(b - c)} + \sqrt{c(a - c)}.\]

1
2
3
+
4
5
6
-
7
8
9
$\frac{a}{b}$
.
0
=
%

$a^n$
$a^{\circ}$
$a_n$
$\sqrt{}$
$\sqrt[n]{}$
$\pi$
$\ln{}$
$\log$
$\theta$
$\sin{}$
$\cos{}$
$\tan{}$

$($
$)$
$[$
$]$
$\cap$
$\cup$
$,$
$\infty$