the-circle-represents-a-farm-where-LK-is-symetric-axe-of-circle-such-as-M-of-this-circle-verifying-ML-2-4MK-2-0-with-LK-150m-calculate-the-radius-of-circle-please-help-me-

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Question Number 78316 by mathocean1 last updated on 15/Jan/20

$$\mathrm{the}\mathrm{circle}\mathrm{represents}\mathrm{a}\mathrm{farm}\mathrm{where}$$$$\left(\mathrm{LK}\right)\mathrm{is}\mathrm{symetric}\mathrm{axe}\mathrm{of}\mathrm{circle}\mathrm{such}$$$$\mathrm{as}\mathrm{\forall }\mathrm{M}\mathrm{of}\mathrm{this}\mathrm{circle}\mathrm{verifying}$$$${\mathrm{ML}}^2-{4\mathrm{MK}}^2=0\mathrm{with}\mathrm{LK}=150\mathrm{m}.$$$$\mathrm{calculate}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{circle}.$$$$\mathrm{please}\mathrm{help}\mathrm{me}\dots$$

Commented by mathocean1 last updated on 15/Jan/20

Commented by john santu last updated on 16/Jan/20

$$M(x,y),L(-15,0),K(0,0)$$$${ML}^2={(x+15)}^2+y^2$$$${MK}^2=x^2+y^2$$$${ML}^2=4{MK}^2$$$${(x+15)}^2+y^2=4x^2+4y^2$$$$x^2+30x+225+y^2=4x^2+4y^2$$$$3x^2+3y^2-30x-225=0$$$$x^2+y^2-10x-225=0$$$$acirclewithcenterpoint(5,0)$$$$radius=\sqrt{25+225}=\sqrt{250}=5\sqrt{10}.$$

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