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May 20th, 2012, 07:20 AM   #1
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Find center of a circle

Hi there,

I'm working as a programmer and need some help.

The point P1 is at the end of a line, the line has the angle At1. The point P2 is at the beginning of a line with the angle At2. I know the coordinates for P1 and P2. I also know the angles At1 and At2. A radius is formed between P1 and P2 and I need to know the center point Pc for the (invisible) circle the which is formed with P1, P2, At1 and At2. The points P1 and P2 can be anywhere in a 2D coordinate system.

Describing image: http://thomashellstrom.com/centerpoint.png

//Thomas
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May 20th, 2012, 01:59 PM   #2
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Re: Find center of a circle

There are a few method of doing this, one of which is the following:

You know that the normal to a circle or part of a circle will go through it's centre. Given the two angles you can calculate angle (and therefore the slope) of two linear graphs with the following properties: both graphs go through the centre of the circle and through one of the other given points each. Knowing two points on a graph, or one point and the slope, makes it possible to derive it's function. Since the two graphs are linear, simply calculate the point of intersection, which evidently is the centre of the circle.

The two angles also makes it possible to calculate the angle P1-PC-P2. Using Pythagora's theorem (a known angle and a known side of a right-angled triangle) you can calculate the radius of the circle (the hypotenuse of this triangle). Now, imagine that this radius belongs to circles centered at P1 and P2, respectively, instead. Set the equations for these circles equal and you will be able to solve this equation for two different set of coordinates (where the two circles intersect) and you should be able to determine which one is the right one.
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May 23rd, 2012, 11:23 PM   #3
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Re: Find center of a circle

I don't know what got into me, it is of course not supposed to be pythagora's theorem. You should use sine
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