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Arian Cole
Posts:
1
From:
somewhere on southamerica
Registered:
5/31/16


Distance from a fixed point to a circle
Posted:
Aug 14, 2017 11:02 PM


There is a fixed point P(x_p,y_p), and a fixed circle C_(O,R), distance from P to variable point A(x,y) is r.Also there is a point K(x_k,y_k) that AK perpendicular to OP. Then R^2OK^2=r^2KP^2 but KP=OPOK; R^2OK^2=r^2(OPOK)^2 r^2R^2=OP^22OP*OK OK=OP/2+(R^2r^2)/2OP KP=OP/2(R^2r^2)/2OP :r^2=R^2+(OP/2(R^2r^2)/2OP)^2+(OP/2+(R^2r^2)/2OP)^2 According to wolfram alfa the solution is https://www.wolframalpha.cominput?i=r%5E2%3DR%5E2%2B(2d+(R%5E2)%2Br%5E2)%2Fd)%5E2+d%2B((R%5E2)%2Br%5E2)%2Fd)%5E2 Acording to me it was an equation in R^4+R^2, whatever be the solution what most shocks me is that r is suposed to vary on A, ((xx_o)^2+(yy_o)^2)) but in r^2=R^2+(OP/2(R^2r^2)/2OP)^2+(OP/2+(R^2r^2)/2OP)^2 OP and R are both fixed as C_(OR) and P are fixed. Is it me or is geometry not working?



