你应该检查圆心到点的距离是否小于半径

使用Python

if (x-center_x)**2 + (y-center_y)**2 <= radius**2:
    # inside circle

iOS 15，接受的答案写在Swift 5.5

func isInRectangle(center: CGPoint, radius: Double, point: CGPoint) -> Bool
{
    return point.x >= center.x - radius && point.x <= center.x + radius &&
    point.y >= center.y - radius && point.y <= center.y + radius
}

//test if coordinate (x, y) is within a radius from coordinate (center_x, center_y)
func isPointInCircle(center: CGPoint,
                     radius:Double, point: CGPoint) -> Bool
{
    if(isInRectangle(center: center, radius: radius, point: point))
    {
        var dx:Double = center.x - point.x
        var dy:Double = center.y - point.y
        dx *= dx
        dy *= dy
        let distanceSquared:Double = dx + dy
        let radiusSquared:Double = radius * radius
        return distanceSquared <= radiusSquared
    }
    return false
}

你应该检查圆心到点的距离是否小于半径

使用Python

if (x-center_x)**2 + (y-center_y)**2 <= radius**2:
    # inside circle

PHP

if ((($x - $center_x) ** 2 + ($y - $center_y) ** 2) <=  $radius **2) {
    return true; // Inside
} else {
    return false; // Outside
}

如前所述，为了显示点是否在圆中，我们可以使用下面的方法

if ((x-center_x)^2 + (y - center_y)^2 < radius^2) {
    in.circle <- "True"
} else {
    in.circle <- "False"
}

要用图形表示，我们可以使用:

plot(x, y, asp = 1, xlim = c(-1, 1), ylim = c(-1, 1), col = ifelse((x-center_x)^2 + (y - center_y)^2 < radius^2,'green','red'))
draw.circle(0, 0, 1, nv = 1000, border = NULL, col = NA, lty = 1, lwd = 1)

我在c#中的回答是一个完整的剪切和粘贴(未优化)解决方案:

public static bool PointIsWithinCircle(double circleRadius, double circleCenterPointX, double circleCenterPointY, double pointToCheckX, double pointToCheckY)
{
    return (Math.Pow(pointToCheckX - circleCenterPointX, 2) + Math.Pow(pointToCheckY - circleCenterPointY, 2)) < (Math.Pow(circleRadius, 2));
}

用法:

if (!PointIsWithinCircle(3, 3, 3, .5, .5)) { }