For \(\Delta ABC\) right-angled triangle at  \(A\) have \(AB=AC\), uppose in the triangle that the point M satisfies \(\widehat{MBA}=\widehat{MAC}=\widehat{MCB}\). Calculate the ratio of \(MA: MB: MC\)

Given \(a,b,c\) are non-negative numbers such that \(ab+bc+ca=1\). Find the minimize value of \(P=\dfrac{1}{\sqrt{a^2+b^2}}+\dfrac{1}{\sqrt{b^2+c^2}}+\dfrac{1}{\sqrt{c^2+a^2}}\)

Given $a,b,c>0$. Prove that $\frac{a^3b}{3a+b}+\frac{b^3c}{3b+c}+\frac{c^3a}{3c+a}\ge \frac{a^2bc}{2a+b+c}+\frac{ab^2c}{a+2b+c}+\frac{abc^2}{a+b+2c}$

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I tried AM-GM but unsuccess