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

AI Thread Summary
To find the coordinates of point B on a circle when given point A, the radius, the slope of the tangent line at A, and the arc direction to B, one can determine the center of the circle using the perpendicular radius at A. The center lies along this radius at a known distance, resulting in two potential center points. By utilizing the direction of the arc between A and B, one can select the correct center point. This method effectively narrows down the possibilities for locating point B. The discussion highlights the geometric relationships involved in solving this problem.
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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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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.
 
Thanks mathman. I just needed a little insight, and you have provided that quickly and succinctly.
 

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