{"version":9,"randomSeed":"3a95a1d97ff7e1d3a766a4810c2b9566","graph":{"viewport":{"xmin":4.417517552899748,"ymin":-0.9776909741419917,"xmax":7.662122559538098,"ymax":2.1686388900385856}},"expressions":{"list":[{"type":"folder","id":"38","title":"circle A"},{"type":"expression","id":"30","folderId":"38","color":"#388c46","latex":"A=\\left(3.64,1.6\\right)"},{"type":"expression","id":"32","folderId":"38","color":"#000000","latex":"r_{1}=2.98","slider":{"hardMin":true,"hardMax":true,"min":"0"}},{"type":"expression","id":"34","folderId":"38","color":"#2d70b3","latex":"\\operatorname{distance}\\left(\\left(x,y\\right),A\\right)=r_{1}"},{"type":"expression","id":"40","folderId":"38","color":"#2d70b3","latex":"\\left(x-A.x\\right)^{2}+\\left(y-A.y\\right)^{2}=r_{1}^{2}"},{"type":"expression","id":"42","folderId":"38","color":"#388c46","latex":"x^{2}-\\left(2A.x\\right)x+A.x^{2}+y^{2}-\\left(2A.y\\right)y+A.y^{2}-r_{1}^{2}=0"},{"type":"folder","id":"41","title":"circle B"},{"type":"expression","id":"31","folderId":"41","color":"#6042a6","latex":"B=\\left(6.9,0.7\\right)"},{"type":"expression","id":"33","folderId":"41","color":"#c74440","latex":"r_{2}=2","slider":{"hardMin":true,"hardMax":true,"min":"0"}},{"type":"expression","id":"35","folderId":"41","color":"#388c46","latex":"\\operatorname{distance}\\left(\\left(x,y\\right),B\\right)=r_{2}"},{"type":"expression","id":"43","folderId":"41","color":"#6042a6","latex":"\\left(x-B.x\\right)^{2}+\\left(y-B.y\\right)^{2}=r_{2}^{2}"},{"type":"expression","id":"44","folderId":"41","color":"#000000","latex":"x^{2}-\\left(2B.x\\right)x+B.x^{2}+y^{2}-\\left(2B.y\\right)y+B.y^{2}-r_{2}^{2}=0"},{"type":"folder","id":"52","title":"solving circle A"},{"type":"expression","id":"53","folderId":"52","color":"#2d70b3","latex":"y=\\left[-1,1\\right]\\sqrt{r_{1}^{2}-\\left(x-A.x\\right)^{2}}+A.y"},{"type":"folder","id":"46","title":"substitution"},{"type":"expression","id":"54","folderId":"46","color":"#388c46","latex":"x^{2}-\\left(2B.x\\right)x+B.x^{2}+\\left(\\left[-1,1\\right]\\sqrt{r_{1}^{2}-\\left(x-A.x\\right)^{2}}+A.y\\right)^{2}-\\left(2B.y\\right)\\left(\\left[-1,1\\right]\\sqrt{r_{1}^{2}-\\left(x-A.x\\right)^{2}}+A.y\\right)+B.y^{2}-r_{2}^{2}=0"},{"type":"text","id":"58","folderId":"46","text":"select a root to use"},{"type":"expression","id":"56","folderId":"46","color":"#000000","latex":"p=-1","slider":{"hardMin":true,"hardMax":true,"min":"-1","max":"1","step":"2"}},{"type":"expression","id":"55","folderId":"46","color":"#6042a6","latex":"x^{2}-\\left(2B.x\\right)x+B.x^{2}+\\left(p\\sqrt{r_{1}^{2}-\\left(x-A.x\\right)^{2}}+A.y\\right)^{2}-\\left(2B.y\\right)\\left(p\\sqrt{r_{1}^{2}-\\left(x-A.x\\right)^{2}}+A.y\\right)+B.y^{2}-r_{2}^{2}=0"},{"type":"expression","id":"59","folderId":"46","color":"#2d70b3","latex":"x^{2}-\\left(2B.x\\right)x+B.x^{2}+\\left(r_{1}^{2}-\\left(x-A.x\\right)^{2}+2pA.y\\sqrt{r_{1}^{2}-\\left(x-A.x\\right)^{2}}+A.y^{2}\\right)-\\left(2B.y\\right)\\left(p\\sqrt{r_{1}^{2}-\\left(x-A.x\\right)^{2}}+A.y\\right)+B.y^{2}-r_{2}^{2}=0"},{"type":"expression","id":"60","folderId":"46","color":"#388c46","latex":"x^{2}-\\left(2B.x\\right)x+B.x^{2}+\\left(r_{1}^{2}-x^{2}+\\left(2A.x\\right)x-A.x^{2}+2pA.y\\sqrt{r_{1}^{2}-\\left(x-A.x\\right)^{2}}+A.y^{2}\\right)-\\left(2B.y\\right)\\left(p\\sqrt{r_{1}^{2}-\\left(x-A.x\\right)^{2}}+A.y\\right)+B.y^{2}-r_{2}^{2}=0"},{"type":"expression","id":"61","folderId":"46","color":"#6042a6","latex":"u=\\sqrt{r_{1}^{2}-\\left(x-A.x\\right)^{2}}","hidden":true},{"type":"expression","id":"62","folderId":"46","color":"#000000","latex":"x^{2}-\\left(2B.x\\right)x+B.x^{2}+\\left(r_{1}^{2}-x^{2}+\\left(2A.x\\right)x-A.x^{2}+2pA.y\\cdot u+A.y^{2}\\right)-\\left(2B.y\\right)\\left(pu+A.y\\right)+B.y^{2}-r_{2}^{2}=0"},{"type":"expression","id":"63","folderId":"46","color":"#c74440","latex":"x^{2}-\\left(2B.x\\right)x+B.x^{2}+-x^{2}+\\left(2A.x\\right)x-A.x^{2}+2pA.y\\cdot u+A.y^{2}+r_{1}^{2}-\\left(2B.y\\right)\\left(pu\\right)-\\left(2B.y\\right)\\left(A.y\\right)+B.y^{2}-r_{2}^{2}=0"},{"type":"expression","id":"64","folderId":"46","color":"#2d70b3","latex":"\\left(2A.x-2B.x\\right)x+\\left(B.x^{2}-A.x^{2}+A.y^{2}+B.y^{2}+r_{1}^{2}-r_{2}^{2}-2A.yB.y\\right)+2pu\\left(A.y-B.y\\right)=0"},{"type":"expression","id":"65","folderId":"46","color":"#c74440","latex":"2\\left(A.x-B.x\\right)x+\\left(B.x^{2}-A.x^{2}+A.y^{2}+B.y^{2}+r_{1}^{2}-r_{2}^{2}-2A.yB.y\\right)=-2pu\\left(A.y-B.y\\right)"},{"type":"expression","id":"67","folderId":"46","color":"#388c46","latex":"4\\left(A.x-B.x\\right)^{2}x^{2}+4\\left(A.x-B.x\\right)\\left(B.x^{2}-A.x^{2}+A.y^{2}+B.y^{2}+r_{1}^{2}-r_{2}^{2}-2A.yB.y\\right)x+\\left(B.x^{2}-A.x^{2}+A.y^{2}+B.y^{2}+r_{1}^{2}-r_{2}^{2}-2A.yB.y\\right)^{2}=4u^{2}\\left(A.y-B.y\\right)^{2}"},{"type":"expression","id":"68","folderId":"46","color":"#6042a6","latex":"u_{a}=4\\left(A.x-B.x\\right)^{2}"},{"type":"expression","id":"69","folderId":"46","color":"#000000","latex":"u_{b}=4\\left(A.x-B.x\\right)\\left(B.x^{2}-A.x^{2}+A.y^{2}+B.y^{2}+r_{1}^{2}-r_{2}^{2}-2A.yB.y\\right)"},{"type":"expression","id":"70","folderId":"46","color":"#c74440","latex":"u_{c}=\\left(B.x^{2}-A.x^{2}+A.y^{2}+B.y^{2}+r_{1}^{2}-r_{2}^{2}-2A.yB.y\\right)^{2}"},{"type":"expression","id":"72","folderId":"46","color":"#388c46","latex":"u_{a}x^{2}+u_{b}x+u_{c}=4u^{2}\\left(A.y-B.y\\right)^{2}"},{"type":"expression","id":"73","folderId":"46","color":"#c74440","latex":"u_{a}x^{2}+u_{b}x+u_{c}=4\\left(r_{1}^{2}-\\left(x-A.x\\right)^{2}\\right)\\left(A.y-B.y\\right)^{2}"}]}}