**Can we find a unique vertex using additional information?**

Hello Thanks for the useful diagrams and solutions.

I have some more informations.

1) The Triangle is on a sphere whose center and Radius is known.

2) One end point of triangle is center of sphere ie, (0,0,0)

3) Second end point also I have.

4) I have to find the third end point.

5) I have a line that is perpendicular to one side of triangle, connecting the unknown vertex and (0,0,0) vertex. So using the direction cosines l1l2+m1m2+n1n2=0 property, I can check out of all vertices which is the valid vertex.

So I would like to know the method of finding the third vertex (eventhough infinite many solutions) from the available sides and angles and two vertices known,also the triangle is on a sphere .(Worried)