The vertex of a great circle is the maximum latitude point of the great circle.

**The vertex has the following properties:**

**There is a maximum latitude point in both the northern and southern hemispheres; these points have the same value of latitude (eg if northern vertex = 40°N then southern vertex = 40°S). The longitudes of the vertices are 180° apart (e.g. if one is in 20°W, the other is in 160°E).**

**At the vertex the course on the great circle is exactly 090°T or 270°T, depending on whether you are proceeding towards the east or the west. This means that the angle between the great circle and the meridian at the vertex is always 90°.**

**In other words we can define vertex as:**

The vertex is the point on a great circle that is closest to the pole; by knowing the latitude of the vertex, if it is too high.

**There are two vertices on a great circle, 180° apart; the nearer vertex is usually the chosen one for navigational calculation.**

**The vertex’s latitude is always numerically equal to or greater than the latitude of any other point on the great circle, including the latitude of departure and destination.**

*Note:*

*Note:*

*To find the position of the vertex you will first have to find the great circle initial course angle A. This will be found by the cosine rule. **We will then know two parts of the triangle and can find any other part. The parts we know are Angle A and the Co-Latitude of A (PA).*

*We need to find PV (when taken from 90°, PV will give the latitude of the vertex), and angle VPA (the D.long between A and V) which is applied to the known longitude of A to give the longitude of the vertex.*

Latitute of vertex:

Sin Mid Part= Cos opposite parts

Sin PV = (Cos Co A x Cos Co PA)

Sin PV = (Sin A x Sin PA)

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