Need help animating an image follow a circular path in JavaFX

I'm working on a university project where I have to recreate the game of musical chairs, I'm at the part of animating the kids going in a circle around chairs. I have been trying to make a test with a rectangle following a circular path.
The problem is that I have an HBox with a tools bar that the mini game will need for later and the rectangle with the path in an stackpane, this two things are in a VBox that basically is the root. But the rectangle does the animation in the bottom right corner of the window and I would like to make it at the center of the stackpane. Any help would be apreciated. Here is the code:

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package javafxapplication4;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import javafx.animation.PathTransition;
import javafx.animation.PathTransition.OrientationType;
import javafx.animation.Timeline;
import javafx.application.Application;
import javafx.event.ActionEvent;
import javafx.event.EventHandler;
import javafx.geometry.Insets;
import javafx.geometry.Pos;
import javafx.scene.Scene;
import javafx.scene.control.Button;
import javafx.scene.control.Label;
import javafx.scene.image.Image;
import javafx.scene.image.ImageView;
import javafx.scene.layout.Background;
import javafx.scene.layout.BackgroundFill;
import javafx.scene.layout.CornerRadii;
import javafx.scene.layout.GridPane;
import javafx.scene.layout.HBox;
import javafx.scene.layout.Pane;
import javafx.scene.layout.Priority;
import javafx.scene.layout.StackPane;
import javafx.scene.layout.VBox;
import javafx.scene.paint.Color;
import javafx.scene.shape.ArcTo;
import javafx.scene.shape.ClosePath;
import javafx.scene.shape.MoveTo;
import javafx.scene.shape.Path;
import javafx.scene.shape.Rectangle;
import javafx.stage.Stage;
import javafx.util.Duration;
import logica.CircularPane;
/**
*
* @author Franklin
*/
public class JavaFXApplication4 extends Application {
@Override
public void start(Stage primaryStage) throws FileNotFoundException {
VBox boxmaster=new VBox();
StackPane stackpane=new StackPane();
HBox tools=new HBox(); tools.setPrefHeight(70);
//Botones y tool bar
//start
Button start=new Button();
start.setPadding(new Insets(-1,-1,-1,-1));
start.setAlignment(Pos.CENTER_LEFT);
tools.getChildren().add(start);
//Cambio de dirección
HBox botones=new HBox(); botones.setSpacing(5);
botones.setAlignment(Pos.CENTER_RIGHT);
//izquierda
Button left=new Button();
left.setPadding(new Insets(-1,-1,-1,-1));
left.setStyle("-fx-background-radius: 5em; " +
"-fx-min-width: 50px; " +
"-fx-min-height: 50px; " +
"-fx-max-width: 50px; " +
"-fx-max-height: 50px;");
botones.getChildren().add(left);
//derecha
Button right=new Button();
right.setPadding(new Insets(-1,-1,-1,-1));
right.setStyle("-fx-background-radius: 5em; " +
"-fx-min-width: 50px; " +
"-fx-min-height: 50px; " +
"-fx-max-width: 50px; " +
"-fx-max-height: 50px;");
botones.getChildren().add(right);
//Pause
Button pause=new Button();
pause.setPadding(new Insets(-1,-1,-1,-1));
pause.setStyle("-fx-background-radius: 5em; " +
"-fx-min-width: 50px; " +
"-fx-min-height: 50px; " +
"-fx-max-width: 50px; " +
"-fx-max-height: 50px;");
botones.getChildren().add(pause);
//Salir
Button exit=new Button(); 
exit.setStyle("-fx-background-radius: 5em; " +
"-fx-min-width: 55px; " +
"-fx-min-height: 55px; " +
"-fx-max-width: 55px; " +
"-fx-max-height: 55px;");
exit.setVisible(false);
botones.getChildren().add(exit);
HBox.setHgrow(botones, Priority.ALWAYS);
HBox.setMargin(start, new Insets(14,0,0,40));
tools.getChildren().add(botones);
tools.setPadding(new Insets(2));
boxmaster.getChildren().add(tools);
//Juego como tal
Rectangle rect2 = new Rectangle(20, 20);
rect2.setArcHeight(10);
rect2.setArcWidth(10);
rect2.setFill(Color.GREEN);
stackpane.getChildren().add(rect2);
Path path2 = createEllipsePath(0, 0, 150, 150, 0);
stackpane.getChildren().add(path2);
PathTransition pathCircle=new PathTransition();
pathCircle.setDuration(Duration.seconds(2));
pathCircle.setPath(path2);
pathCircle.setNode(rect2);
pathCircle.setOrientation(OrientationType.ORTHOGONAL_TO_TANGENT);
pathCircle.setCycleCount(Timeline.INDEFINITE);
pathCircle.setAutoReverse(false);
stackpane.setAlignment(Pos.CENTER);
boxmaster.getChildren().add(stackpane);
VBox.setVgrow(stackpane, Priority.ALWAYS);
Scene scene=new Scene(boxmaster,1080,720);
primaryStage.setScene(scene);
primaryStage.setResizable(false);
primaryStage.show();
pathCircle.play();
}
private Path createEllipsePath(double centerX, double centerY, double radiusX, double radiusY, double rotate)
{
ArcTo arcTo = new ArcTo();
arcTo.setX(centerX - radiusX + 1); // to simulate a full 360 degree celcius circle.
arcTo.setY(centerY - radiusY);
arcTo.setSweepFlag(false);
arcTo.setLargeArcFlag(true);
arcTo.setRadiusX(radiusX);
arcTo.setRadiusY(radiusY);
arcTo.setXAxisRotation(rotate);
Path path = new Path();
path.getElements().addAll(
new MoveTo(centerX - radiusX, centerY - radiusY),
arcTo,
new ClosePath()); // close 1 px gap.
path.setStroke(Color.DODGERBLUE);
path.getStrokeDashArray().setAll(5d, 5d);
return path;
}
/**
* @param args the command line arguments
*/
public static void main(String[] args) {
launch(args);
}
}

NOTES= The createEllipsePath code is what I found after digging on how to create a circular path.
The buttons do not have text, because originally they have a graphic.

I'm not an expert in JavaFX. I just played around with your code and I got it to do what I think (and hope) you want it to do. I added an extra Path. The first Path draws the circle and the second Path is assigned to the PathTransition. I then played around with the coordinates of the second Path until I got the green rectangle to move around the circle that is the first path.

Note that I removed unused imports from your code and added a different letter to each of your Buttons just so I could see where they appear in the Scene.

Here is the code.

public class JavaFXApplication4 extends Application {

    @Override
    public void start(Stage primaryStage) { //throws FileNotFoundException {
        VBox boxmaster = new VBox();
        StackPane stackpane = new StackPane();
        HBox tools = new HBox();
        tools.setPrefHeight(70);

        //Botones y tool bar

        //start

        Button start = new Button("S");
        start.setPadding(new Insets(-1,-1,-1,-1));
        start.setAlignment(Pos.CENTER_LEFT);
        tools.getChildren().add(start);

        //Cambio de dirección
        HBox botones = new HBox();
        botones.setSpacing(5);
        botones.setAlignment(Pos.CENTER_RIGHT);
        //izquierda
        
        Button left = new Button("L");
        left.setPadding(new Insets(-1,-1,-1,-1));
        left.setStyle("-fx-background-radius: 5em; " +
                      "-fx-min-width: 50px; " +
                      "-fx-min-height: 50px; " +
                      "-fx-max-width: 50px; " +
                      "-fx-max-height: 50px;");
        botones.getChildren().add(left);
        
        //derecha
        
        Button right = new Button("R");
        right.setPadding(new Insets(-1,-1,-1,-1));
        right.setStyle("-fx-background-radius: 5em; " +
                       "-fx-min-width: 50px; " +
                       "-fx-min-height: 50px; " +
                       "-fx-max-width: 50px; " +
                       "-fx-max-height: 50px;");
        botones.getChildren().add(right);
        
        //Pause
        
        Button pause = new Button("P");
        pause.setPadding(new Insets(-1,-1,-1,-1));
        pause.setStyle("-fx-background-radius: 5em; " +
                       "-fx-min-width: 50px; " +
                       "-fx-min-height: 50px; " +
                       "-fx-max-width: 50px; " +
                       "-fx-max-height: 50px;");
        botones.getChildren().add(pause);
        
        //Salir
        Button exit = new Button("E");
        exit.setStyle("-fx-background-radius: 5em; " +
                      "-fx-min-width: 55px; " +
                      "-fx-min-height: 55px; " +
                      "-fx-max-width: 55px; " +
                      "-fx-max-height: 55px;");
        exit.setVisible(false);
        botones.getChildren().add(exit);
        
        HBox.setHgrow(botones, Priority.ALWAYS);
        HBox.setMargin(start, new Insets(14, 0, 0, 40));
        
        tools.getChildren().add(botones);
        tools.setPadding(new Insets(2));
        
        boxmaster.getChildren().add(tools);
        
        //Juego como tal
        Rectangle rect2 = new Rectangle(20, 20);
        rect2.setArcHeight(10);
        rect2.setArcWidth(10);
        rect2.setFill(Color.GREEN);
        stackpane.getChildren().add(rect2);
        
        Path path2 = createEllipsePath(166, 10, 160, 160, 0);  // changed this line.
        Path path1 = createEllipsePath(0, 0, 150, 150, 0);  // added this line.
        stackpane.getChildren().add(path1);
        
        PathTransition pathCircle = new PathTransition();
        pathCircle.setDuration(Duration.seconds(2));
        pathCircle.setPath(path2);
        pathCircle.setNode(rect2);
        pathCircle.setOrientation(OrientationType.ORTHOGONAL_TO_TANGENT);
        pathCircle.setCycleCount(Timeline.INDEFINITE);
        pathCircle.setAutoReverse(false);
        
        stackpane.setAlignment(Pos.CENTER);
        boxmaster.getChildren().add(stackpane);
        VBox.setVgrow(stackpane, Priority.ALWAYS);
        Scene scene=new Scene(boxmaster,1080,720);
        primaryStage.setScene(scene);
        primaryStage.setResizable(false);
        primaryStage.show();
        pathCircle.play();
    }
    
    private Path createEllipsePath(double centerX, double centerY, double radiusX, double radiusY, double rotate)
    {
        ArcTo arcTo = new ArcTo();
        arcTo.setX(centerX - radiusX + 1); // to simulate a full 360 degree celcius circle.
        arcTo.setY(centerY - radiusY);
        arcTo.setSweepFlag(false);
        arcTo.setLargeArcFlag(true);
        arcTo.setRadiusX(radiusX);
        arcTo.setRadiusY(radiusY);
        arcTo.setXAxisRotation(rotate);

        Path path = new Path();
        path.getElements().addAll(
                new MoveTo(centerX - radiusX, centerY - radiusY),
                arcTo,
                new ClosePath()); // close 1 px gap.
        path.setStroke(Color.DODGERBLUE);
        path.getStrokeDashArray().setAll(5d, 5d);
        return path;
    }

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        launch(args);
    }
}