> -----Original Message----- > From: Martin Peach [mailto:martinrp@vax2.concordia.ca] > > ----- Original Message ----- > From: "Jafta" > To: > Sent: Thursday, January 10, 2002 2:58 PM > Subject: Re: [PIC]Find center point of circle? > > > > Let's try this: > > 1. Draw a line through the 2 points > > 2. Where the line intersects the circle, draw a circle > around each > point > > 3. Draw a line through the intersection of these circles > > 4. Where this line intersects the 1st circle, draw a > circle around each > > point > > Which was the first circle? The one we don't know? > > > 5. Draw a line between the intersections of these circles > > 6. Where the line in (5) and (3) intersect, is that not > the center? > > For a given radius there are always two possible circles that > go through two > arbitrary points unless the points are exactly two radii > apart. There is > just not enough information available to resolve the matter > no matter how > many circles and lines you draw. Actually, if you open the problem up to drawing circles of a given radius around two arbitrary points, there are four possibilities: 1. The two points are the same, so both circles intersect at all of their points. 2. The two points are twice the radius apart, so the circles intersect at one point. 3. The two points are unique and less than twice the radius apart, so the circles intersect at two points. 4. The two points are greater twice the radius apart, so the circles don't intersect. The way the original problem was stated, the two points are on a circle of a given radius. That allows for case 1, 2, or 3. If it's case 1, you can't solve the problem. If it's case 2, the center of the original circle is the point of intersection between the two circles. Case 3 is the interesting one. I haven't come up with a formal proof, but I believe that the center of the original circle is the point of intersection closest to the line through your two initial points. -Mike -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email listserv@mitvma.mit.edu with SET PICList DIGEST in the body