Bonsoir,
Les triangles OPN et RPS sont semblables.
[tex]\dfrac{PS}{PN}=\dfrac{SR}{ON}\\\\\dfrac{PS}{3+\sqrt{3}}=\dfrac{3-\sqrt{3}}{\sqrt{2}}\\\\PS=(3+\sqrt{3})\times\dfrac{3-\sqrt{3}}{\sqrt{2}}\\\\PS=\dfrac{(3+\sqrt{3})(3-\sqrt{3})}{\sqrt{2}}\\\\PS=\dfrac{3^2-(\sqrt{3})^2}{\sqrt{2}}\\\\PS=\dfrac{9-3}{\sqrt{2}}\\\\PS=\dfrac{6}{\sqrt{2}}\\\\PS=\dfrac{6\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}\\\\PS=\dfrac{6\sqrt{2}}{2}\\\\PS=3\sqrt{2}[/tex]
