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So this question is very similar to this question.

I have given two points on a circle, and the angle at which the circle passes the first point. My goal is to find the angle at which the circle passes the 2nd point. enter image description here In my sketch, we see that the line of the circle is leaving P1 at a 90-degree angle. I will use this for this example

Explanation: We know: P1 P2

From that we know:

x ($P2.x - P1.x$)

y ($P2.y - P1.y$)

d ($√(x² + y²)$)

what I want to get is $α$ so I guess I need the radius, but that's where my math ends.

Please tell me if you need any further information, or if I did not provide any info correctly Thanks

Edit: Okay so what i didnt say is that the Y Value of P1 is always 0, so a horizontal line can pass through P1 and M

HobbyDev
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    "the angle at which the circle passes" is an ambiguous description. Please fix that. –  Nov 21 '21 at 11:40
  • yes I know but i dont know how i should describe this in a better way – HobbyDev Nov 21 '21 at 12:34
  • Could you label the angle you mean? I’m guessing it’s not α, which you say you need to get. You also remark that “the line of the circle is leaving P1 at a 90-degree angle”, but that can’t be it either, because that’s always true (the circle, or its tangent, is always at 90° to its radius). So what/where is the angle that you say we’re given? – Tim Pederick Nov 21 '21 at 12:39
  • Okay so what i didnt say is that the Y Value of P1 is always 0, so the 90-degree value has to be true, right? – HobbyDev Nov 21 '21 at 12:49
  • Yep, that’s important: we’re given a (horizontal) line through P1 and the centre M. That, plus the two points, is enough to locate M. (But the line isn’t necessary for that 90° angle. Imagine we had a non-horizontal line through P1 and M… and then you rotated your page so that it became horizontal. It was always 90°.) – Tim Pederick Nov 21 '21 at 12:55

1 Answers1

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Hint...you will need to establish the coordinates of the centre of the circle. You can do this by writing down the equation of the perpendicular bisector of $P_1P_2$ and finding where it intersects the horizontal line through $P_1$. Once you know the coordinates of the centre, it is just a matter of simple trigonometry to establish the angle $\alpha$.

David Quinn
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  • Ou thanks for that hint, that makes sense to me, but how am I going to check where it will intersect with the line of P1? I would have to get the y level of the perpendicular bisector, and then calculate the x value of it, right? – HobbyDev Nov 21 '21 at 12:36
  • @HobbyDev Your horizontal line is $y=0$, yeah? So when you have the equation of a line, how do you find the point where it intersects $y=0$? – Tim Pederick Nov 21 '21 at 13:01
  • i read my comment again and it doesnt make any sense, you are right. – HobbyDev Nov 21 '21 at 13:19