Given the co-ordinates (x,y) of a center of a circle and it's radius. determine whether a point lies inside the circle or outside the circle? Tell three formlaes which are used in this question?

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The equation of a circle with given centre (x0,y0) and radius r is given by:

(x-x0)²+(y-y0)²=r²

implicitly, this equations makes use of the equation of distance between two points (x,y) and (x0,y0):
Distance = sqrt((x-x0)²+(y-y0)²)

If the distance from the centre is greater than r, then it is outside the circle. If the distance is less than r, then it is inside the circle.
I.e.
Point P1(x1,y1) is outside, on, or inside the circle if
(x1-x0)²+(y1-y0)²
is greater than, equal to, or less than
r².

To determine whether a point lies inside or outside a circle, you can use the distance formula to find the distance between the center of the circle and the given point. If the distance is less than the radius, the point lies inside the circle; if it is equal to the radius, the point lies on the circle; and if it is greater than the radius, the point lies outside the circle.

Here are the three formulas used in this question:

1. Distance Formula:
The distance between two points (x1, y1) and (x2, y2) can be calculated using the following formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

2. Circle Equation:
The equation of a circle with center (h, k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2

3. Comparing distance and radius:
To determine whether a point (x, y) lies inside, on, or outside the circle with center (h, k) and radius r, compare the calculated distance to the radius:
- If distance < r: The point is inside the circle.
- If distance = r: The point lies on the circle.
- If distance > r: The point is outside the circle.

By using these formulas, you can determine the position of a given point relative to a circle.