Circle passing through a point and tangential to two curves

//Increase num for higher precision//Will fail if too low and take too long if too highnum = 15;â€‹//Centers of circles that are tangential and equidistant to the input Curvespt1 = c1.PointAtParameter(0..1..#num);pt2 = c2.PointAtParameter(0..1..#num);pl1 = Plane.ByThreePoints(c1.CenterPoint,c1.CenterPoint.Translate(0,0,1),pt1);vc1 = Vector.ByTwoPoints(c2.CenterPoint,pt2);pt3 = Point.PruneDuplicates(List.Flatten(pt2.Project(pl1<1>,vc1<2>),-1),0.01);ds1 = Math.Round(pt3<1>.DistanceTo(pt1<2>),1);ds2 = Math.Round(pt3<1>.DistanceTo(pt2<2>),1);pt4 = List.FilterByBoolMask(pt3,List.AllFalse((ds1==ds2)<1>))["out"];â€‹//Centers that are equidistant to the input Curves and Pointds3 = Math.Round(pt4<1>.DistanceTo(c1<2>),1);ds4 = Math.Round(pt4<1>.DistanceTo(c2<2>),1);ds5 = Math.Round(pt4<1>.DistanceTo(p1<2>),1);pt5 = List.FilterByBoolMask(pt4,ds3==ds5 && ds4==ds5)["in"];ds6 = pt5.DistanceTo(p1);cr1 = Circle.ByCenterPointRadius(pt5,ds6);â€‹//Geometry Color[GeometryColor.ByGeometryColor(p1,Color.ByARGB(255,255,0,0)),GeometryColor.ByGeometryColor(c1,Color.ByARGB(255,0,255,0)),GeometryColor.ByGeometryColor(c2,Color.ByARGB(255,0,0,255)),GeometryColor.ByGeometryColor(cr1[0],Color.ByARGB(255,255,0,255))];

//Curve 1c1 = Arc.ByThreePoints(Point.ByCoordinates(-3,2),Point.ByCoordinates(2,1),Point.ByCoordinates(5,3));â€‹// Curve 2c2 = Arc.ByThreePoints(Point.ByCoordinates(-6,2),Point.ByCoordinates(-4,1),Point.ByCoordinates(0,3));â€‹//Pointp1 = Point.ByCoordinates(-2,1);â€‹//Limit length of arcs as much as possible//Will fail if no circle passes through the point//Multiple circles that satisfy the condition possible

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