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Re: Bisectors and MPP - for 3 sights, equivalent to circle method
From: Bill Noyce
Date: 2003 May 29, 14:11 -0400
From: Bill Noyce
Date: 2003 May 29, 14:11 -0400
Doug Royer explains how to use angle bisectors to find the MPP for a round of three or four (or more?) sights, and wonders whether it's more or less precise than the method that finds a circle that just touches each LOP. For three sights, the three bisectors all meet at a point, which is also the center of the circle that will just touch each LOP. Therefore, for three sights the methods are equivalent. To see this, imagine we have LOP's labeled A, B, and C, with bisectors AB, BC, and CA. Consider the point where AB intersects BC. Its distance from A is equal to its distance from B, because it is on bisector AB. And its distance from B is equal to its distance from C, because it is on bisector BC. Therefore its distance from A is equal to its distance from C, so it must also be on bisector CA. The only point where all three distances are the same is the center of the circle that is tangent to all three bisectors (as long as we are on the proper side of each LOP, and both methods ensure that). -- Bill