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On 6/4/2011 1:38 PM, Greg Rudzinski wrote:
>
> Micheal Dorl wrote:
>
> " it would seem that the other angles would enter
> into the solution. Surely there are other positions from which the
> angle between A & B are the same but with different bearings."
>
> Every point on the arc of position will have the same difference
> between the bearings to mark A and B. When determining the radius of
> the circle half the distance between A and B is used so that two right
> triangles are formed with the hypotenuse of each being the radius of
> the circle. The half distance represents the opposite side so simple
> trig will give you the Radius(hypotenuse) = 1/2 distance(opposite) A-B
> divided by SIN of observed angle A-B. The radius is then used to plot
> the circle center on the chart arcing an intersection off A and B.
> From the circle center the full circle can be made which will have the
> observer, mark A and B on the perimeter. Getting a fix requires
> plotting a second circle between mark C and A or B. If variation and
> deviation are known then a single bearing to A or B can be plotted to
> intersect the circle to produce a fix. The intersection of two
> horizontal angle circles is the better fix though. See David Fleming's
> previous post for additional explanations and a description of the
> standard method for plotting the horizontal angle circle.
>
> Greg Rudzinski
>

Ok, I had to rediscover Proposition III.20 from Euclid's Elements
regarding the relationship between an arc inscribed on the circumference
of a circle and the central angle.   I'm convinced now.

   

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