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Find the coordinates of a point on a circle without knowing the center point.

by b1gd0g
Tags: circle, coordinates, knowing, point
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b1gd0g
#1
Sep9-11, 03:20 PM
P: 2
Given 2 points on a circle, call them A and B. I know the cartesian coordinates of A. I also know the radius of the circle, the slope of the tangent line at A, and the length and direction of the arc between A and B. I don't know the coordiates of the center of the circle.

How do I find the coordinates of point B?
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mathman
#2
Sep9-11, 03:26 PM
Sci Advisor
P: 6,035
The radius at A is perpendicular to the tangent line. The center is along the radius at a known distance. There are only two possible points. Use the information about B (direction of arc??) to choose the location of the center.
b1gd0g
#3
Sep9-11, 03:31 PM
P: 2
Thanks mathman. I just needed a little insight, and you have provided that quickly and succinctly.


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