What is the name of the point where the two nappes of a right circular come meet

It is the vertex. It can also be called the apex but that has a connotation of being the top-most point so is not appropriate.

You are given an ore ship that is traveling west toward Duluth on Lake Superior at 18 miles per hour with a bearing of 285deg Split Rock Lighthouse. Also, after 1 hour the bearing of the lighthouse is 340deg. The distance between the ship and the lighthouse when the second bearing is determined is 35 miles.