{"version":9,"randomSeed":"98f366a285fa7ed51844c79bb0f2f977","graph":{"viewport":{"xmin":-2.5000000000000018,"ymin":-2.499999999999999,"xmax":2.4999999999999982,"ymax":2.500000000000001}},"expressions":{"list":[{"type":"expression","id":"1","color":"#c74440","latex":"A=1","labelSize":"medium"},{"type":"expression","id":"3","color":"#388c46","latex":"B=0"},{"type":"expression","id":"4","color":"#6042a6","latex":"C=1"},{"type":"expression","id":"5","color":"#000000","latex":"D=1","labelSize":"medium"},{"type":"expression","id":"6","color":"#c74440","latex":"E=-0.5"},{"type":"expression","id":"8","color":"#388c46","latex":"F=-0.5"},{"type":"expression","id":"9","color":"#c74440","latex":"\\left(A,B\\right)"},{"type":"expression","id":"10","color":"#388c46","latex":"\\left(C,D\\right)"},{"type":"expression","id":"11","color":"#2d70b3","latex":"\\left(E,F\\right)"},{"type":"expression","id":"12","color":"#2d70b3","latex":"\\left(C-A\\right)\\left(x-\\frac{A+C}{2}\\right)+\\left(D-B\\right)\\left(y-\\frac{B+D}{2}\\right)=0","labelSize":"medium"},{"type":"expression","id":"13","color":"#388c46","latex":"\\left(C-A\\right)x+\\left(D-B\\right)y=\\frac{1}{2}\\left(\\left(C+A\\right)\\left(C-A\\right)+\\left(D+B\\right)\\left(D-B\\right)\\right)","labelSize":"medium"},{"type":"expression","id":"14","color":"#6042a6","latex":"\\left(C-A\\right)x+\\left(D-B\\right)y=\\frac{1}{2}\\left(C^{2}-A^{2}+D^{2}-B^{2}\\right)"},{"type":"expression","id":"15","color":"#000000","latex":"\\left(E-A\\right)x+\\left(F-B\\right)y=\\frac{1}{2}\\left(E^{2}-A^{2}+F^{2}-B^{2}\\right)"},{"type":"text","id":"20","text":"turns out this is the same solution as i did last time, but the derivation is simpler"},{"type":"expression","id":"18","color":"#2d70b3","latex":"s_{0}=\\frac{\\left(\\frac{1}{2}\\left(C^{2}-A^{2}+D^{2}-B^{2}\\right)\\left(F-B\\right)-\\frac{1}{2}\\left(E^{2}-A^{2}+F^{2}-B^{2}\\right)\\left(D-B\\right),\\frac{1}{2}\\left(E^{2}-A^{2}+F^{2}-B^{2}\\right)\\left(C-A\\right)-\\frac{1}{2}\\left(C^{2}-A^{2}+D^{2}-B^{2}\\right)\\left(E-A\\right)\\right)}{\\left(C-A\\right)\\left(F-B\\right)-\\left(D-B\\right)\\left(E-A\\right)}"},{"type":"text","id":"22","text":"\"simplified\" forms (you can't make this simple, can you)"},{"type":"expression","id":"23","color":"#000000","latex":"s_{1}=\\frac{\\left(\\left(C^{2}-A^{2}+D^{2}-B^{2}\\right)\\left(F-B\\right)-\\left(E^{2}-A^{2}+F^{2}-B^{2}\\right)\\left(D-B\\right),\\left(E^{2}-A^{2}+F^{2}-B^{2}\\right)\\left(C-A\\right)-\\left(C^{2}-A^{2}+D^{2}-B^{2}\\right)\\left(E-A\\right)\\right)}{2\\left(CF-BC-AF+AB-DE+AD+BE-AB\\right)}"},{"type":"expression","id":"24","color":"#c74440","latex":"s_{2}=\\frac{\\left(\\left(C^{2}-A^{2}+D^{2}-B^{2}\\right)\\left(F-B\\right)-\\left(E^{2}-A^{2}+F^{2}-B^{2}\\right)\\left(D-B\\right),\\left(E^{2}-A^{2}+F^{2}-B^{2}\\right)\\left(C-A\\right)-\\left(C^{2}-A^{2}+D^{2}-B^{2}\\right)\\left(E-A\\right)\\right)}{2\\left(CF-BC-AF-DE+AD+BE\\right)}"},{"type":"expression","id":"25","color":"#2d70b3","latex":"\\operatorname{distance}\\left(\\left(x,y\\right),s_{2}\\right)=\\operatorname{distance}\\left(\\left(A,B\\right),s_{2}\\right)"}]}}