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    Re: Horizontal Angle and the Hand Bearing Compass
    From: Michael Dorl
    Date: 2011 Jun 04, 15:11 -0500

    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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