Question

How do I find all points of a circle, given the radius and the coordinates of the center point?

Answer 1

The equation of a circle is (x-h)^2 + (y -k)^2 = r^2.
Where:

x = x-coordinate
y = y-coordinate
h = x-coordinate of the center point
k = y-coordinate of the center point
r = radius

Because the distance from the center to a point on the circumference on the x-axis, the y-axis and the radius form a right angled triangle where the x-Distance is the base, y-distance is the height and r is the hypotenuse of that right angled triangle. For a circle with center (0,0) the equation of a circle is x^2 + y^2 = r^2 (which is the Pythagorean Theorem).

You could also use the identities cos theta = y/r => y = r*cos theta and sin theta = x/y => x = r*sin theta and iterate over theta from 0 to 360 degrees

So given a center point (h,k) and radius r you can find the points (x,y) that lie on the circumference of the circle.

Then you can have a function to check if a certain point lies in a within the circumference or not. What exactly do you need this for?