I'm no mathmetician so forgive my wording when I ask this, there is no doubt an answer somewhere but I dont even know what to search for.

intersection of arc

I want to find the intersection point (B) as a Vector2 on a perfect circle.

If I know X, Y, A and C I assume I can use the radius and distance to calulate the position of B based on the distance between X and C somehow? (using C# if there are any methods which will accomplish this)


  • \$\begingroup\$ Is the distance YX the same as XA? Do X and A always have the same y value (are they both at the same height)? \$\endgroup\$ – Leo Mar 6 '18 at 16:04
  • \$\begingroup\$ Yes, someone informed me I can use Pythagoras, seems simple now! \$\endgroup\$ – Col.Cook Mar 6 '18 at 16:21
  • \$\begingroup\$ I have been trying to write an answer but I'm terrible at explaining trigonometry using English :) \$\endgroup\$ – Leo Mar 6 '18 at 16:25
  • \$\begingroup\$ Me too, I think just saying Pythagoras is enough to lead to the right direction, I put my code below \$\endgroup\$ – Col.Cook Mar 6 '18 at 16:26

I used Pythagoras to solve it

here is the code I used:

    // X placement can be anywhere along the x axis of the object
    float xPlacement = Random.Range(0, obstacleWidth);
    // Get the distance from the middle of the arc as a positive number and the max height of the arc(obstacle height) 
    // Use Pythagoras to equate b
    float b = Mathf.Sqrt(Mathf.Pow(obstacleHeight, 2) - Mathf.Pow(Mathf.Abs((xPlacement - (obstacleWidth / 2))), 2));
    Vector2 intersect = new Vector2(xPlacement, b);
  • \$\begingroup\$ And if that somehow didn't work, I'm sure the SOHCAHTOA would. \$\endgroup\$ – Draco18s Mar 6 '18 at 19:34

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