Four particles each of mass M, move along a circle of radius R...

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${F}_{\text{net}} = {F}_{1} + 2{F}_{2}\cos 45 °$

$= \dfrac{G{M}^{2}}{( 2R{)}^{2}} + 2 \times \dfrac{G{M}^{2}}{( \sqrt{2}R{)}^{2}} \times \dfrac{1}{\sqrt{2}} = \dfrac{G{M}^{2}}{4{R}^{2}} + \dfrac{G{M}^{2}}{\sqrt{2}{R}^{2}} = \dfrac{( 4 + \sqrt{2} ) G{M}^{2}}{4\sqrt{2}{R}^{2}}$

Now ${F}_{C} = {F}_{\text{net}}$

$\dfrac{M{V}^{2}}{R} = \dfrac{( 4 + \sqrt{2} ) G{M}^{2}}{4\sqrt{2}{R}^{2}}$

$V = \sqrt{\dfrac{( 4 + \sqrt{2} )}{4\sqrt{2}}\dfrac{GM}{R}}$