Calculate if a Circle intersects a Arc

Question

Have a Cartesian Plane

cartesian plane

And a Arc with the measures:

point = 200, 200
radius = 50
start angle = 0
end angle = 180 

And a Circle with the measures:

point = 220, 230
radius = 3 

How can I calculate the Circle intersects the Arc at some point? As the picture attached

Thank you

Answer 1

It is hard to figure out your data and relate the units used in your attached diagram.

Assuming that “point = 220, 230; radius = 3” means the center of the circle is at (200, 230) and its radius = 3 units, then the equation of that circle is $(x – 220)^2 + (y – 230)^2 = 3^2$.

The arc is just part of a circle, and therefore its equation can also be similarly established.

Solve these two equations will give you the (normally two) points of intersection. You have to test which one is the required.