UIBezierPath Rotation around a UIView's center

I'm creating a custom UIView, in which I implement its draw(rect:) method by drawing a circle with a large width using UIBezierPath, that draw a square on the top (as shown in the picture, don't consider the colors or the size). Then I try creating rotated copies of the square, to match a "settings" icon (picture 2, consider only the outer ring). To do that last thing, I need to rotate the square using a CGAffineTransform(rotationAngle:) but the problem is that this rotation's center is the origin of the frame, and not the center of the circle. How can I create a rotation around a certain point in my view?

As a demonstration of @DuncanC's answer (up voted), here is the drawing of a gear using CGAffineTransforms to rotate the gear tooth around the center of the circle:

class Gear: UIView {
    var lineWidth: CGFloat = 16
    let boxWidth: CGFloat = 20
    let toothAngle: CGFloat = 45

    override func draw(_ rect: CGRect) {

        let radius = (min(bounds.width, bounds.height) - lineWidth) / 4.0

        var path = UIBezierPath()
        path.lineWidth = lineWidth
        UIColor.white.set()

        // Use the center of the bounds not the center of the frame to ensure
        // this draws correctly no matter the location of the view
        // (thanks @dulgan for pointing this out)
        let center = CGPoint(x: bounds.maxX / 2, y: bounds.maxY / 2)

        // Draw circle
        path.move(to: CGPoint(x: center.x + radius, y: center.y))
        path.addArc(withCenter: CGPoint(x: center.x, y: center.y), radius: radius, startAngle: 0, endAngle: 2 * .pi, clockwise: true)
        path.stroke()

        // Box for gear tooth
        path = UIBezierPath()
        let point = CGPoint(x: center.x - boxWidth / 2.0, y: center.y - radius)
        path.move(to: point)
        path.addLine(to: CGPoint(x: point.x, y: point.y - boxWidth))
        path.addLine(to: CGPoint(x: point.x + boxWidth, y: point.y - boxWidth))
        path.addLine(to: CGPoint(x: point.x + boxWidth, y: point.y))
        path.close()
        UIColor.red.set()

        // Draw a tooth every toothAngle degrees
        for _ in stride(from: toothAngle, through: 360, by: toothAngle) {
            // Move origin to center of the circle
            path.apply(CGAffineTransform(translationX: -center.x, y: -center.y))

            // Rotate
            path.apply(CGAffineTransform(rotationAngle: toothAngle * .pi / 180))

            // Move origin back to original location
            path.apply(CGAffineTransform(translationX: center.x, y: center.y))

            // Draw the tooth
            path.fill()
        }
    }
}

let view = Gear(frame: CGRect(x: 0, y: 0, width: 200, height: 200))

Here it is running in a Playground: