Talk:Line circle intersection

Error by vb.net

i try to use the vb.net-code but in following constellation is a error

center=10,10 radius=5 line from 5,0 to 5,20

there is no intersection - but it is a point of tangent.

regards Jan

It seems the task author did not include test examples where there is a tangent. --Wherrera (talk) 18:42, 20 October 2022 (UTC)

Worth adding to the draft task --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 $x=\pm {\sqrt {2}},\;y=\pm {\sqrt {2}}$.

Ignoring the negative x and y results for simplicity, and working through the wolfram approach:

$r=1,\;x_{1}=0,\;y_{1}=0,\;x_{2}=1,\;y_{2}=1$

$d_{x}=1,\;d_{y}=1,\;d_{r}={\sqrt {1^{2}+1^{2}}}={\sqrt {2}},\;D=0$

$x={{d_{x}{\sqrt {r^{2}d_{r}^{2}-0}}} \over {d_{r}^{2}}}={{\sqrt {2}} \over {2}}$

$y={{d_{y}{\sqrt {r^{2}d_{r}^{2}-0}}} \over {d_{r}^{2}}}={{\sqrt {2}} \over {2}}$

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. --Rdm (talk) 12:59, 21 October 2022 (UTC)