I have an arc of a circle, and I have some other point in space (this might lie on the arc or it might not). I am looking for a formula that will compute the closest point on the arc to the other point. I also need to be able to get the distance from the start of the arc to this closest point.what I know about the arc is: (1) the circle centre, (2) the angle of the beginning of the arc, (3) the arc angle, (4) the circle radius, (5) begin and end points of the arc on the circle circumference, (6) the direction the arc is going (i.e. Clockwise or Counter-clockwise)what I know about the other point is: (1) its position

Question

Eleanor Luna · Accepted Answer

You know that the points on the arc has a constant distance of   r to the center of the circle. Given any &quot;other point&quot;, the line starting from the center of the circle and ending at that point is known and fixed. And the third line of the triangle (sometimes those three points are in a line, and thus is not a triangle strictly speaking) formed by those three points are the distance you need.Thus, all you need to do is the rotate the line connecting the arc and center of the circle, and get the smallest length for the third line.Notice there are several cases for &quot;the other point&quot; to stay, e.g. within the angle of the arc and within the range of   r, or could be within the angle of the arc but outside the range of   r, or outside the range of the angle of the arc, etc.

I have an arc of a circle, and I have some other point in space (this might lie on the arc or it mig

Answered question

Answer & Explanation

New Questions in High school geometry