Python: Checking If Coordinates Are Within Circle [duplicate]

Question

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Closed 8 years ago.

Possible Duplicate:
How can I make Turtle recognize a circle?

I have a function that draws a few circles and I am going to place dots inside them. Depending if the dot falls within the circle, depends on wether the colour will change or not.

The biggest issue I am finding is how to check whether or not the dot is within the circle. Does anyone have any idea how to calculate coordinates within a circle or is their a method which can check coordinates against the circle?

Answer 1

1. Compute (Euclidean) distance to the circle's center,

   sqrt((x - center_x) ** 2 + (y - center_y) ** 2)
   

2. Check whether the result is less than the radius.

Answer 2

For a circle with center (x,y) and radius r, a point (x1, y1) is within the circle if

(x1-x)² + (y1-y)² <= r²

Answer 3

To check if a coordinate lies on a circle you can use the equation of the circle

a² + b² = r²

So to check if the point is inside the circle:

a² + b² <= r²