[color=#c51414]Ever wondered what the equation is for moving points from inside of a circle to outside of a circle? [b]To see how this works, move the point P[/b].[/color] O is the circle's center, and P is any point in the circle. P' is the inverse of P, and displays what happens to a point when you invert the circle. Explore the way point P and P' interact with each other and with point O. Click the check box 'view line'. Line e will appear, move P along this line to view how P' changes in relation to P.
How does P react with P' when you move them around? How does P react with P' when you move them across the line e? [color=#1551b5][b]Definition:[/b] taking points inside of the circle, and moving them outside of the circle[/color] [list][*]For a circle with center O, every fixed point inside of the circle is called P [*]For every point P, there is a point P’ outside of the circle that follows the property that the distance from O to P multiplied by the distance from O to P’ must equal the r2 (r being the radius of the circle) [color=#198f88][b]Equation:[/b] OP x OP’ = r2[/color] [*]If P is inside of the circle, then P’ will always be outside of the circle [*]If P moves away from O, then P’ will move towards O [*]if P is on the point O, ([color=#888]P=O[/color]), then P’ does not exist [*]Every point of the circle itself is fixed, and will not be inverted. [/list]