The distance between the circumcenter and the orthocenter of the triangle whose vertices are (0, 0), (6, 8), and (4,3) is Z. Then the value of $\frac{\mathrm{L}}{\sqrt{5}}$ is _________ .

Given vertices of triangle are o(0,0), B(6,8), and c(-4,3).
Slope of OB = $\frac{8}{6}$
Slope of OC = $-\frac{3}{4}$
$\therefore \mathrm{\angle }\mathrm{BOC}=\frac{\mathrm{\pi }}{2}$
$\mathrm{\Delta OBC}$ is right-angled at O.
Circumcenter = Midpoint of hypotenuse BC = $\left(1,\frac{11}{2}\right)$
Orthocenter - Vertex O(0, 0)
Required distance = $\sqrt{\left(1+\frac{121}{4}\right)}=\frac{5\sqrt{5}}{2} \mathrm{units}$