$\Delta MPN$ vuông tại $P$, đường cao $PH$$\\$ $\Rightarrow PH^2=MH.NH$ $S_{\Delta MPN}=S_{\Delta MPH}+S_{\Delta NPH}=150=\dfrac{1}{2}PH.MN(1)\\ S_{\Delta MPH}.S_{\Delta NPH}=\dfrac{1}{4}PH^2.MH.NH=\dfrac{1}{4}PH^4=5184\\ \Rightarrow PH=12(2)\\ (1)(2)\Rightarrow MN=25\Rightarrow R=12,5$