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Question Number 34585 by tawa tawa last updated on 08/May/18

Commented by Rasheed.Sindhi last updated on 08/May/18

$$\mathcal{N}otrelatedtoabove....$$$$\text{You can't use 'macro parameter character \#' in math mode}$$$$\mathrm{a}\mathrm{perfect}\mathrm{square}.{\mathrm{I}}^{\prime }\mathrm{ve}\mathrm{tried}\mathrm{to}\mathrm{provide}$$$$\mathrm{a}\mathrm{proof}.\mathrm{Anyone}\mathrm{who}\mathrm{is}\mathrm{interested}\mathrm{in}\mathrm{the}$$$$\mathrm{question}\mathrm{can}\mathrm{see}\mathrm{my}\mathrm{proof}.\mathrm{Critical}$$$$\mathrm{comments}\mathrm{will}\mathrm{be}\mathrm{welcomed}.$$

Answered by MJS last updated on 09/May/18

$$r_0=4$$$$M_0{M}_1=M_0{M}_2=r_1=r_2=2$$$$M_0{M}_3=r_0-r_3$$$$M_1{M}_3=M_2{M}_3=r_1+r_3$$$${\left(M_0{M}_1\right)}^2+{\left(M_0{M}_3\right)}^2={\left(M_1{M}_3\right)}^2$$$$2^2+{(4-r_3)}^2={(2+r_3)}^2$$$$4+16-8r_3+r_3^2=4+4r_3+r_3^2$$$$16=12r_3$$$$r_3=\frac{4}{3}$$

Commented by Joel578 last updated on 09/May/18

$$whatisM?$$

Commented by MJS last updated on 09/May/18

$$\mathrm{the}\mathrm{centers}\mathrm{of}\mathrm{the}\mathrm{circles}.\mathrm{sorry},\mathrm{my}\mathrm{language}$$$$\mathrm{is}\mathrm{German}\mathrm{center}\mathrm{is}‘‘{\mathrm{Mittelpunkt}}^{″}\mathrm{in}\mathrm{German}$$$$\mathrm{so}\mathrm{without}\mathrm{further}\mathrm{thinking},M\mathrm{seemed}\mathrm{natural}...$$

Commented by Joel578 last updated on 10/May/18

$$okay,thankyou$$

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