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:: Worth adding to the draft task --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 11:26, 21 October 2022 (UTC)
== The Wolfram approach ==
The task currently references https://mathworld.wolfram.com/Circle-LineIntersection.html which (for now, at least) seems to be incorrect.
Consider, for example, a circle of radius 1 at the origin and a line extending through the origin and the point x=1, y=1. Here, we expect intersections at <math>x=\pm \sqrt{2},\;y=\pm\sqrt{2}</math>.
Ignoring the negative x and y results for simplicity, and working through the wolfram approach:
<math>r = 1,\; x_1=0,\; y_1=0,\; x_2=1,\; y_2=1</math>
<math>d_x = 1,\; d_y = 1,\; d_r = \sqrt{1^{2}+1^{2}} = \sqrt{2},\; D = 0</math>
<math>x = {{d_x \sqrt{r^{2}d_r^{2}-0}} \over {d_r^{2}}} = {{\sqrt{2}} \over {2}}</math>
<math>y = {{d_y \sqrt{r^{2}d_r^{2}-0}} \over {d_r^{2}}} = {{\sqrt{2}} \over {2}}</math>
I'd like to believe that I'm wrong here -- past experience suggests I make mistakes far more often than anything in Wolfram. But I keep going over this and not seeing where I went wrong. --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 12:59, 21 October 2022 (UTC)
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