Random point in circle method is not uniformly distributed

I have the following method in Java:

public static Vector2d random(Circle circle) {
    // this returns a random number between 0 and Math.PI * 2
    double angle = MathUtils.random(0, Math.PI * 2);
    // give the point inside the unit circle
    // this returns a normalized vector from a given angle
    Vector2d point = new Vector2d(angle);
    // however, this is only along the edge
    // now add a random magnitude (because this is a normalized vector, we can just multiply it by the desired magnitude)
    double magnitude = Math.random();
    point = point.multiply(magnitude);
    // now expand this to fit the radius
    point = point.multiply(circle.getRadius());
    // now translate by circleCenter
    return point.add(circle.getCenter());
}

This does return a point in the defined circle, however, when you do this many times and plot the points, you can clearly see most points will be toward the center.

Why is this? I don't see how my math can do this.

Comment if you want me to add an image of the points on the plot, if you think that could be helpful.