I am working on a GPS problem involving Longitude and Latitude. I have 3 waypoints making a triangle and I need to find the center and the cooresponding coordinates to that center.

A= N 44.18.642
w 76.33.807

B= N 44.18.362
w 76.34.163

C= N 44.18.313
w 76.33.383


I know you draw a circle that touches on each point, but how can I derive a set of GPS ccordinates to find the location?

I'm not following the problem here, so let me try to restate it in a different way. You are looking to find the center of a traingle whose three vertices are located at the cordinates you provided- is that right? The center of a traingle is defined as the point at the intersection of the bisectors of the triangle's three vertices - see the attached figure. So I don't understand what you are talking about with respect to circles touching each point, as the distance from the center to the three vertices could all be different.

The method I would propose to you is as follows:

1. Calculate the formula for a line that passes through point A and bisects angle BAC (the red dotted line in the figure). You can do this by finding the bearings from point A to points B and C, and from this calculate the bearing that is the bisector of angle BAC.

2. Do the same for point B: determine the formula for the line that bisects the angle ABC (the blue dotted line).

3. Find the intersection point for these two bisector lines. This is the center point of the triangle.

4. You can check by finding the bisector of angle ACB and verifying that it passes through the intersection point.

Hope this helps.

Quote:

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Originally Posted by ebaines

... Find the intersection point for these two bisector lines. This is the center point of the triangle...

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:)

I have to laugh because on the previous problem you found a really ingenious way to do that proof without any serious analytical work.

While your technique for this problem is absolutely correct, you can also find the center point of a triangle by simply averaging the respective x- and y-coordinates of the three points.

Quote:

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Originally Posted by jcaron2

:)

I have to laugh because on the previous problem you found a really ingenious way to do that proof without any serious analytical work.

While your technique for this problem is absolutely correct, you can also find the center point of a triangle by simply averaging the respective x- and y-coordinates of the three points.

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I think we're both wrong! On further reflection I think what the OP is asking for is how to find a point that is equidistant from the 3 corners of the triangle. The center as I defined it in my original response is really the center of gravity for the triangle, but this point is not (typically) equidistant from the three vertices.

The way to do this is a bit different from what I wrote. See the attached figure - any point that is equidistant from vertices A and B will lie along a line that is perpendicular to line AB and that intersects AB at the midpoint. Similarly, the point must also be on the line that is perpendicular to BC and intercepts BC at the midpoint. So you've got two lines - find the intersection point between them, and you have the point in question. Check by making sure the point lies along the perpendicular bisector of AC.

Now that I reread it also, I think you must be right. Nicely done.