[Solved] Locate coordinate from angle from n nautical miles

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//Example with mutliple coordinates before creating an arc. AREA DEFINED AS 133830N1450807E TO 132836N1444449E TO 133043N1443814E TO 133515N1443710E THEN CLOCKWISE ON A 15.3 NM ARC CENTERED ON 133416N1445256E TO THE POINT OF ORIGIN
                    //Abbreviation
                    //    a
                    //    b
                    //    m(midangle)   (cx,cy,ax,ay,bx,by)
                    //    x(lat)
                    //    y(long)
                    //Xc=latitude provided in text for center point
                    //Yc=longitude provided in text for center point

                    //point is the last point
                    var startPointStr = generateCircleLine[generateCircleLine.Length - 1].Split(' ');

                    var startPoint = new TfrXY { LngX = Convert.ToDouble(startPointStr[0]), LatY = Convert.ToDouble(startPointStr[1]) };
                    //point before the last point

                    var stopPointStr = generateCircleLine[generateCircleLine.Length - 2].Split(' ');

                    var stopPoint = new TfrXY { LngX = Convert.ToDouble(stopPointStr[0]), LatY = Convert.ToDouble(stopPointStr[1]) };
                    var centerPoint = new TfrXY { LngX = Convert.ToDouble(centerPointStr[0]), LatY = Convert.ToDouble(centerPointStr[1]) };

                    var a = Math.Atan2(stopPoint.LatY- centerPoint.LatY, stopPoint.LngX-centerPoint.LngX);
                    var b = Math.Atan2(startPoint.LatY-centerPoint.LatY, startPoint.LngX-centerPoint.LngX);

                    var m = MidAngle(centerPoint.LngX, centerPoint.LatY, startPoint.LngX, startPoint.LatY, stopPoint.LngX, stopPoint.LatY);

                    var d = Math.Sqrt(      
                        Math.Pow(Convert.ToDouble(centerPointStr[0]) - startPoint.LngX, 2) +
                        Math.Pow(Convert.ToDouble(centerPointStr[1]) - startPoint.LatY, 2)   );

                    var ym = (centerPoint.LatY) +( d * Math.Sin(m));
                    var xm = (centerPoint.LngX) + (d * Math.Cos(m));








The latidude and longitude would be  ym  and xml

You will also need to use this function.



        /// <summary>
        /// Find mid angle
        /// </summary>
        /// <param name="cx">center point longitude</param>
        /// <param name="cy">center point latitude</param>
        /// <param name="ax">Starting point longitude </param>
        /// <param name="ay">Starting point latitude</param>
        /// <param name="bx">Stopping point longitude</param>
        /// <param name="by">Stopping point latitude</param>
        /// <returns></returns>
        public static double MidAngle(double cx, double cy, double ax, double ay, double bx, double by)
        {

            var a = Math.Atan2(ay - cy, ax - cx);
            var b = Math.Atan2(by - cy, bx - cy);

            //Fixing infinite loop issue
            if ((ax == cx) && (ay > cy))
                a = Math.PI / 2.0;
            else if ((ax == cx) && (ay <= cy))
                a = -Math.PI / 2.0;
            else
                a = Math.Atan2(ay - cy, ax - cx);

            if ((bx == cx) && (by > cy))
                b = Math.PI / 2.0;
            else if ((bx == cx) && (by <= cy))
                b = -Math.PI / 2.0;
            else
                b = Math.Atan2(by - cy, bx - cx);



            var delta = a - b;
            while (delta < 0)
            {
                delta += 2 * Math.PI;
            }
            return a - (delta / 2);
        }

solved Locate coordinate from angle from n nautical miles