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Given $2$ points (limited length), and a point with angle(unlimited). How do I check if they will intersect or not?

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I've only been able to find line-line or $4$ points intersections.

Current progress :

line-angle: $y-x = \cot(d) * (x-mx)$
point-point: $(y-b)(c-a) = (x-a)(d-b)$ # sorry the d here is from (c,d), not the angle

How can I merge these together? Thank you

Cookie
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  • you have two different $d$s here. Maybe re-label the diagram? BTW why not just check the angles from $(x,y)$ to each endpoint and see if angle $d$ lies between? – David Quinn Oct 19 '21 at 11:34
  • Sorry only cot(d) means the angle. To your advice, I still cannot get the intersection points even if I knows it intersects :( – Cookie Oct 19 '21 at 12:05
  • If you're trying to find the intersection points it would be better if you named the point $(x,y)$ as $(x_0,y_0)$ instead so you can solve simultaneously the equations of the lines. – David Quinn Oct 19 '21 at 13:03

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