How to create great circle arc (B) that is perpendicular to another great circle arc (A)at a specific point on A?

Question

Suppose I only have two vertex points in (longitude,latitude) to make great circle arc A. I would then like to find an arc perpendicular at any given point on A to make up great circle arc B and then find points on B that are a distance x away from A. How do I find these points?

Answer 1

We can combine information from this page

At first calculate bearing A1-A2:

θ = atan2( sin Δλ ⋅ cos φ2 , cos φ1 ⋅ sin φ2 − sin φ1 ⋅ cos φ2 ⋅ cos Δλ )
where   φ1,λ1 is the start point, φ2,λ2 the end point 
(Δλ is the difference in longitude)

Then get perpendicular bearing

θ1 = θ + Pi/2 or
θ2 = θ - Pi/2

Then get destination point using start point A1 and bearing θ1 or θ2

φ2 = asin( sin φ1 ⋅ cos δ + cos φ1 ⋅ sin δ ⋅ cos θ )
λ2 = λ1 + atan2( sin θ ⋅ sin δ ⋅ cos φ1, cos δ − sin φ1 ⋅ sin φ2 )
where   φ is latitude, λ is longitude, 
θ is the bearing (clockwise from north), 
δ is the angular distance d/R; 
d being the distance travelled, R the earth’s radius