I am trying to find coordinates of point $X$ if I know distance from point $A$ and bearing from point $B$, and a line from point $B$ intersects on a circle which radius equals the distance from point $A$ (see images). Is it possible to find it with a formula? Thanks a lot!
The knowns (for Image 1):
Point A coordinates - Latitude: 37.8886778; Longitude: 23.8044972
Point B coordinates - Latitude: 37.9214949; Longitude: 23.9189052
r = 14 nm
d (bearing where 0=North and 90=East) = 50 degrees
If points A and B were the same, I would use the following code to find Point X:
distance = distance / EARTHRADIUS;
heading = deg2rad(heading);
fromLat = deg2rad(latitude);
fromLng = deg2rad(longitude);
cosDistance = Math.cos(distance);
sinDistance = Math.sin(distance);
sinFromLat = Math.sin(fromLat);
cosFromLat = Math.cos(fromLat);
sinLat = cosDistance * sinFromLat + sinDistance * cosFromLat * Math.cos(heading);
dLng = Math.atan2(sinDistance * cosFromLat * Math.sin(heading), cosDistance - sinFromLat * sinLat);
POINT X = rad2deg(Math.asin(sinLat)),rad2deg(fromLng + dLng)
So, I guess it is a question of finding the distance between B and X.