$SO\bot \left( OAB \right)$ Kẻ $SH\bot AB\Rightarrow OH\bot AB$

$\Rightarrow AB\bot \left( SOH \right)\Rightarrow \left( SAB \right)\bot \left( SOH \right)$

Kẻ $OI\bot SH\Rightarrow OI\bot (SAB)$nên d = OI

$\Delta SOA:\text{O}{{\text{S}}^{2}}=64-25=39$

$\Delta OHA:\text{O}{{\text{H}}^{2}}=25-16=9$

$\Rightarrow \frac{1}{O{{I}^{2}}}=\frac{1}{O{{H}^{2}}}+\frac{1}{O{{S}^{2}}}=\frac{1}{9}+\frac{1}{39}=\frac{16}{117}$

$\Rightarrow OI= \frac{3}{4}\sqrt{13}$

Chọn B